SSS2 Maths Lesson 3 Examination

In a circle, the angle subtended by a diameter at the circumference is:

A) \(60^\circ\)

Correct Incorrect Correct answer

B) \(45^\circ\)

Correct Incorrect Correct answer

C) \(90^\circ\)

Correct Incorrect Correct answer

D) \(120^\circ\)

Correct Incorrect Correct answer

The angle subtended by an arc at the center of a circle is \_\_\_\_\_\_\_\_ the angle subtended by it at the circumference.

A) Equal to

Correct Incorrect Correct answer

B) Twice

Correct Incorrect Correct answer

C) Half

Correct Incorrect Correct answer

D) One-third

Correct Incorrect Correct answer

The opposite angles of a cyclic quadrilateral are:

A) Equal

Correct Incorrect Correct answer

B) Supplementary

Correct Incorrect Correct answer

C) Complementary

Correct Incorrect Correct answer

D) Right angles

Correct Incorrect Correct answer

If an arc subtends an angle of \(70^\circ\) at the circumference, what is the angle it subtends at the center?

A) \(70^\circ\)

Correct Incorrect Correct answer

B) \(140^\circ\)

Correct Incorrect Correct answer

C) \(35^\circ\)

Correct Incorrect Correct answer

D) \(210^\circ\)

Correct Incorrect Correct answer

In a circle, the angle in a semicircle is always:

A) \(60^\circ\)

Correct Incorrect Correct answer

B) \(45^\circ\)

Correct Incorrect Correct answer

C) \(90^\circ\)

Correct Incorrect Correct answer

D) \(180^\circ\)

Correct Incorrect Correct answer

If two chords of a circle subtend equal angles at the circumference, they are:

A) Parallel

Correct Incorrect Correct answer

B) Tangents

Correct Incorrect Correct answer

C) Equal in length

Correct Incorrect Correct answer

D) Perpendicular

Correct Incorrect Correct answer

The exterior angle of a cyclic quadrilateral is equal to:

A) Half the interior opposite angle

Correct Incorrect Correct answer

B) Double the interior opposite angle

Correct Incorrect Correct answer

C) The interior opposite angle

Correct Incorrect Correct answer

D) \(180^\circ\) minus the opposite angle

Correct Incorrect Correct answer

In a circle, the perpendicular from the center to a chord:

A) Bisects the radius

Correct Incorrect Correct answer

B) Doubles the chord

Correct Incorrect Correct answer

C) Bisects the chord

Correct Incorrect Correct answer

D) Bisects the arc

Correct Incorrect Correct answer

The sum of the opposite angles of a cyclic quadrilateral is:

A) \(90^\circ\)

Correct Incorrect Correct answer

B) \(270^\circ\)

Correct Incorrect Correct answer

C) \(180^\circ\)

Correct Incorrect Correct answer

D) \(360^\circ\)

Correct Incorrect Correct answer

An angle subtended by the same arc at the circumference in the same segment is:

A) Complementary

Correct Incorrect Correct answer

B) Supplementary

Correct Incorrect Correct answer

C) Equal

Correct Incorrect Correct answer

D) Right angle

Correct Incorrect Correct answer

A quadrilateral is cyclic if and only if:

A) All sides are equal

Correct Incorrect Correct answer

B) Opposite sides are parallel

Correct Incorrect Correct answer

C) Sum of opposite angles is \(180^\circ\)

Correct Incorrect Correct answer

D) It is a rectangle

Correct Incorrect Correct answer

The opposite angles of a cyclic quadrilateral are:

A) Supplementary

Correct Incorrect Correct answer

B) Complementary

Correct Incorrect Correct answer

C) Supplementary

Correct Incorrect Correct answer

D) Right angles

Correct Incorrect Correct answer

In a cyclic quadrilateral \(ABCD\), if \(\angle A = 75^\circ\), find \(\angle C\).

A) \(115^\circ\)

Correct Incorrect Correct answer

B) \(105^\circ\)

Correct Incorrect Correct answer

C) \(105^\circ\)

Correct Incorrect Correct answer

D) \(90^\circ\)

Correct Incorrect Correct answer

Which of these quadrilaterals is always cyclic?

A) Rhombus

Correct Incorrect Correct answer

B) Rectangle

Correct Incorrect Correct answer

C) Parallelogram

Correct Incorrect Correct answer

D) Kite

Correct Incorrect Correct answer

In a cyclic quadrilateral, the exterior angle is equal to:

A) The interior opposite angle

Correct Incorrect Correct answer

B) Half the opposite interior angle

Correct Incorrect Correct answer

C) Sum of two adjacent angles

Correct Incorrect Correct answer

D) \(90^\circ\)

Correct Incorrect Correct answer

In a cyclic quadrilateral \(PQRS\), if \(\angle P = 95^\circ\) and \(\angle Q = 80^\circ\), find \(\angle R\).

A) \(85^\circ\)

Correct Incorrect Correct answer

B) \(100^\circ\)

Correct Incorrect Correct answer

C) \(95^\circ\)

Correct Incorrect Correct answer

D) \(105^\circ\)

Correct Incorrect Correct answer

The diagonals of a cyclic quadrilateral:

A) Are always equal

Correct Incorrect Correct answer

B) Always bisect each other

Correct Incorrect Correct answer

C) Subtend equal angles at the circumference

Correct Incorrect Correct answer

D) Are perpendicular

Correct Incorrect Correct answer

In a cyclic quadrilateral \(WXYZ\), if \(\angle W = 70^\circ\) and \(\angle X = 95^\circ\), find \(\angle Z\).

A) \(100^\circ\)

Correct Incorrect Correct answer

B) \(115^\circ\)

Correct Incorrect Correct answer

C) \(85^\circ\)

Correct Incorrect Correct answer

D) \(90^\circ\)

Correct Incorrect Correct answer

A quadrilateral is cyclic if and only if:

A) It has all equal sides

Correct Incorrect Correct answer

B) Its diagonals are equal

Correct Incorrect Correct answer

C) One pair of opposite angles are supplementary

Correct Incorrect Correct answer

D) All angles are right angles

Correct Incorrect Correct answer

In a cyclic quadrilateral \(LMNO\), \(\angle L = 60^\circ\) and \(\angle M = 110^\circ\). Find \(\angle O\).

A) \(120^\circ\)

Correct Incorrect Correct answer

B) \(115^\circ\)

Correct Incorrect Correct answer

C) \(110^\circ\)

Correct Incorrect Correct answer

D) \(100^\circ\)

Correct Incorrect Correct answer

A quadrilateral is cyclic if and only if:

A) All sides are equal

Correct Incorrect Correct answer

B) Opposite sides are parallel

Correct Incorrect Correct answer

C) Sum of opposite angles is \(180^\circ\)

Correct Incorrect Correct answer

D) It is a rectangle

Correct Incorrect Correct answer

The opposite angles of a cyclic quadrilateral are:

A) Supplementary

Correct Incorrect Correct answer

B) Complementary

Correct Incorrect Correct answer

C) Supplementary

Correct Incorrect Correct answer

D) Right angles

Correct Incorrect Correct answer

In a cyclic quadrilateral \(ABCD\), if \(\angle A = 75^\circ\), find \(\angle C\).

A) \(115^\circ\)

Correct Incorrect Correct answer

B) \(105^\circ\)

Correct Incorrect Correct answer

C) \(105^\circ\)

Correct Incorrect Correct answer

D) \(90^\circ\)

Correct Incorrect Correct answer

Which of these quadrilaterals is always cyclic?

A) Rhombus

Correct Incorrect Correct answer

B) Rectangle

Correct Incorrect Correct answer

C) Parallelogram

Correct Incorrect Correct answer

D) Kite

Correct Incorrect Correct answer

In a cyclic quadrilateral, the exterior angle is equal to:

A) The interior opposite angle

Correct Incorrect Correct answer

B) Half the opposite interior angle

Correct Incorrect Correct answer

C) Sum of two adjacent angles

Correct Incorrect Correct answer

D) \(90^\circ\)

Correct Incorrect Correct answer

In a cyclic quadrilateral \(PQRS\), if \(\angle P = 95^\circ\) and \(\angle Q = 80^\circ\), find \(\angle R\).

A) \(85^\circ\)

Correct Incorrect Correct answer

B) \(100^\circ\)

Correct Incorrect Correct answer

C) \(95^\circ\)

Correct Incorrect Correct answer

D) \(105^\circ\)

Correct Incorrect Correct answer

The diagonals of a cyclic quadrilateral:

A) Are always equal

Correct Incorrect Correct answer

B) Always bisect each other

Correct Incorrect Correct answer

C) Subtend equal angles at the circumference

Correct Incorrect Correct answer

D) Are perpendicular

Correct Incorrect Correct answer

In a cyclic quadrilateral \(WXYZ\), if \(\angle W = 70^\circ\) and \(\angle X = 95^\circ\), find \(\angle Z\).

A) \(100^\circ\)

Correct Incorrect Correct answer

B) \(115^\circ\)

Correct Incorrect Correct answer

C) \(85^\circ\)

Correct Incorrect Correct answer

D) \(90^\circ\)

Correct Incorrect Correct answer

A quadrilateral is cyclic if and only if:

A) It has all equal sides

Correct Incorrect Correct answer

B) Its diagonals are equal

Correct Incorrect Correct answer

C) One pair of opposite angles are supplementary

Correct Incorrect Correct answer

D) All angles are right angles

Correct Incorrect Correct answer

In a cyclic quadrilateral \(LMNO\), \(\angle L = 60^\circ\) and \(\angle M = 110^\circ\). Find \(\angle O\).

A) \(120^\circ\)

Correct Incorrect Correct answer

B) \(115^\circ\)

Correct Incorrect Correct answer

C) \(110^\circ\)

Correct Incorrect Correct answer

D) \(100^\circ\)

Correct Incorrect Correct answer

What is the length of a chord that subtends a \(60^\circ\) angle in a circle of radius 10 cm?

5cm

Correct Incorrect Correct answer

10cm

Correct Incorrect Correct answer

15cm

Correct Incorrect Correct answer

8.66cm

Correct Incorrect Correct answer

If the length of an arc is 20 cm and the radius is 10 cm, what is the angle in degrees subtended by the arc at the center of the circle?

\(60^\circ\)

Correct Incorrect Correct answer

\(90^\circ\)

Correct Incorrect Correct answer

\(120^\circ\)

Correct Incorrect Correct answer

\(180^\circ\)

Correct Incorrect Correct answer

A circle has a radius of 12 cm. What is the length of an arc that subtends a \(90^\circ\) angle at the center?

9.42 cm

Correct Incorrect Correct answer

12cm

Correct Incorrect Correct answer

3\(\pi\) cm

Correct Incorrect Correct answer

6cm

Correct Incorrect Correct answer

If two chords in a circle intersect at a point inside the circle, what is the relationship between the segments formed?

The products of the segments are equal.

Correct Incorrect Correct answer

The segments are equal.

Correct Incorrect Correct answer

The angles are equal.

Correct Incorrect Correct answer

The chords are congruent.

Correct Incorrect Correct answer

A chord divides a circle into two arcs. What is the relationship between the lengths of these arcs?

They are equal if the chord is a diameter.

Correct Incorrect Correct answer

The longer arc subtends the larger angle.

Correct Incorrect Correct answer

The lengths are always equal.

Correct Incorrect Correct answer

Both A and B are correct.

Correct Incorrect Correct answer

In a circle, if two arcs are equal, what can we conclude about the chords that subtend these arcs?

They are equal.

Correct Incorrect Correct answer

They are perpendicular.

Correct Incorrect Correct answer

They are parallel.

Correct Incorrect Correct answer

One is longer than the other.

Correct Incorrect Correct answer

What is the angle subtended by a diameter at the circumference of a circle?

\(90^\circ\)

Correct Incorrect Correct answer

\(60^\circ\)

Correct Incorrect Correct answer

\(120^\circ\)

Correct Incorrect Correct answer

\(180^\circ\)

Correct Incorrect Correct answer

he angle between a tangent and a chord through the point of contact is equal to:

The angle subtended by the chord at the center.

Correct Incorrect Correct answer

The angle subtended by the chord in the alternate segment.

Correct Incorrect Correct answer

The angle subtended by the tangent at the center.

Correct Incorrect Correct answer

None of the above

Correct Incorrect Correct answer

If the radius of a circle is doubled, how does the length of a chord that subtends the same angle at the center change?

It remains the same.

Correct Incorrect Correct answer

It doubles.

Correct Incorrect Correct answer

It quadruples.

Correct Incorrect Correct answer

It is halved.

Correct Incorrect Correct answer

What is the relationship between the arc length and the radius of a circle?

Arc length increases with a decrease in radius.

Correct Incorrect Correct answer

Arc length is directly proportional to the radius.

Correct Incorrect Correct answer

Arc length is inversely proportional to the radius.

Correct Incorrect Correct answer

None of the above.

Correct Incorrect Correct answer

In a circle, the angle subtended by a diameter at the circumference is:

A) \(60^\circ\)

Correct Incorrect Correct answer

B) \(45^\circ\)

Correct Incorrect Correct answer

C) \(90^\circ\)

Correct Incorrect Correct answer

D) \(120^\circ\)

Correct Incorrect Correct answer

The angle subtended by an arc at the center of a circle is \_\_\_\_\_\_\_\_ the angle subtended by it at the circumference.

A) Equal to

Correct Incorrect Correct answer

B) Twice

Correct Incorrect Correct answer

C) Half

Correct Incorrect Correct answer

D) One-third

Correct Incorrect Correct answer

The opposite angles of a cyclic quadrilateral are:

A) Equal

Correct Incorrect Correct answer

B) Supplementary

Correct Incorrect Correct answer

C) Complementary

Correct Incorrect Correct answer

D) Right angles

Correct Incorrect Correct answer

If an arc subtends an angle of \(70^\circ\) at the circumference, what is the angle it subtends at the center?

A) \(70^\circ\)

Correct Incorrect Correct answer

B) \(140^\circ\)

Correct Incorrect Correct answer

C) \(35^\circ\)

Correct Incorrect Correct answer

D) \(210^\circ\)

Correct Incorrect Correct answer

In a circle, the angle in a semicircle is always:

A) \(60^\circ\)

Correct Incorrect Correct answer

B) \(45^\circ\)

Correct Incorrect Correct answer

C) \(90^\circ\)

Correct Incorrect Correct answer

D) \(180^\circ\)

Correct Incorrect Correct answer

If two chords of a circle subtend equal angles at the circumference, they are:

A) Parallel

Correct Incorrect Correct answer

B) Tangents

Correct Incorrect Correct answer

C) Equal in length

Correct Incorrect Correct answer

D) Perpendicular

Correct Incorrect Correct answer

The exterior angle of a cyclic quadrilateral is equal to:

A) Half the interior opposite angle

Correct Incorrect Correct answer

B) Double the interior opposite angle

Correct Incorrect Correct answer

C) The interior opposite angle

Correct Incorrect Correct answer

D) \(180^\circ\) minus the opposite angle

Correct Incorrect Correct answer

In a circle, the perpendicular from the center to a chord:

A) Bisects the radius

Correct Incorrect Correct answer

B) Doubles the chord

Correct Incorrect Correct answer

C) Bisects the chord

Correct Incorrect Correct answer

D) Bisects the arc

Correct Incorrect Correct answer

The sum of the opposite angles of a cyclic quadrilateral is:

A) \(90^\circ\)

Correct Incorrect Correct answer

B) \(270^\circ\)

Correct Incorrect Correct answer

C) \(180^\circ\)

Correct Incorrect Correct answer

D) \(360^\circ\)

Correct Incorrect Correct answer

An angle subtended by the same arc at the circumference in the same segment is:

A) Complementary

Correct Incorrect Correct answer

B) Supplementary

Correct Incorrect Correct answer

C) Equal

Correct Incorrect Correct answer

D) Right angle

Correct Incorrect Correct answer

A quadrilateral is cyclic if and only if:

A) All sides are equal

Correct Incorrect Correct answer

B) Opposite sides are parallel

Correct Incorrect Correct answer

C) Sum of opposite angles is \(180^\circ\)

Correct Incorrect Correct answer

D) It is a rectangle

Correct Incorrect Correct answer

The opposite angles of a cyclic quadrilateral are:

A) Supplementary

Correct Incorrect Correct answer

B) Complementary

Correct Incorrect Correct answer

C) Supplementary

Correct Incorrect Correct answer

D) Right angles

Correct Incorrect Correct answer

In a cyclic quadrilateral \(ABCD\), if \(\angle A = 75^\circ\), find \(\angle C\).

A) \(115^\circ\)

Correct Incorrect Correct answer

B) \(105^\circ\)

Correct Incorrect Correct answer

C) \(105^\circ\)

Correct Incorrect Correct answer

D) \(90^\circ\)

Correct Incorrect Correct answer

Which of these quadrilaterals is always cyclic?

A) Rhombus

Correct Incorrect Correct answer

B) Rectangle

Correct Incorrect Correct answer

C) Parallelogram

Correct Incorrect Correct answer

D) Kite

Correct Incorrect Correct answer

In a cyclic quadrilateral, the exterior angle is equal to:

A) The interior opposite angle

Correct Incorrect Correct answer

B) Half the opposite interior angle

Correct Incorrect Correct answer

C) Sum of two adjacent angles

Correct Incorrect Correct answer

D) \(90^\circ\)

Correct Incorrect Correct answer

In a cyclic quadrilateral \(PQRS\), if \(\angle P = 95^\circ\) and \(\angle Q = 80^\circ\), find \(\angle R\).

A) \(85^\circ\)

Correct Incorrect Correct answer

B) \(100^\circ\)

Correct Incorrect Correct answer

C) \(95^\circ\)

Correct Incorrect Correct answer

D) \(105^\circ\)

Correct Incorrect Correct answer

The diagonals of a cyclic quadrilateral:

A) Are always equal

Correct Incorrect Correct answer

B) Always bisect each other

Correct Incorrect Correct answer

C) Subtend equal angles at the circumference

Correct Incorrect Correct answer

D) Are perpendicular

Correct Incorrect Correct answer

In a cyclic quadrilateral \(WXYZ\), if \(\angle W = 70^\circ\) and \(\angle X = 95^\circ\), find \(\angle Z\).

A) \(100^\circ\)

Correct Incorrect Correct answer

B) \(115^\circ\)

Correct Incorrect Correct answer

C) \(85^\circ\)

Correct Incorrect Correct answer

D) \(90^\circ\)

Correct Incorrect Correct answer

A quadrilateral is cyclic if and only if:

A) It has all equal sides

Correct Incorrect Correct answer

B) Its diagonals are equal

Correct Incorrect Correct answer

C) One pair of opposite angles are supplementary

Correct Incorrect Correct answer

D) All angles are right angles

Correct Incorrect Correct answer

In a cyclic quadrilateral \(LMNO\), \(\angle L = 60^\circ\) and \(\angle M = 110^\circ\). Find \(\angle O\).

A) \(120^\circ\)

Correct Incorrect Correct answer

B) \(115^\circ\)

Correct Incorrect Correct answer

C) \(110^\circ\)

Correct Incorrect Correct answer

D) \(100^\circ\)

Correct Incorrect Correct answer

SSS2 Maths Lesson 3 Examination

Noah Wasiu October 6, 2025

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