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Question (21)

QN009578

The vertices of a square are always:

(A) Collinear
(B) Concyclic
(C) Non-coplanar
(D) Concurrent

Correct Answer: B

Explanation:

Every square is a cyclic quadrilateral.

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Question (22)

QN009579

In cyclic quadrilateral PQRS, ∠P = 68°. Find ∠R.

(A) 102°
(B) 112°
(C) 122°
(D) 132°

Correct Answer: B

Explanation:

∠R = 180°−68°=112°.

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Question (23)

QN009580

A cyclic quadrilateral cannot have opposite angles:

(A) 70° and 110°
(B) 95° and 85°
(C) 120° and 60°
(D) 100° and 100°

Correct Answer: D

Explanation:

Opposite angles must sum to 180°, but 100°+100°=200°.

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Question (24)

QN009581

If four points are concyclic, then they lie on the:

(A) Same line
(B) Same plane only
(C) Same circle
(D) Same diameter

Correct Answer: C

Explanation:

Concyclic points lie on the same circle.

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Question (25)

QN009582

In a cyclic quadrilateral, if ∠A = x° and ∠C = 2x°, then x equals:

(A) 45°
(B) 50°
(C) 60°
(D) 90°

Correct Answer: C

Explanation:

x+2x=180°, so 3x=180° and x=60°.

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Question (26)

QN009583

Which theorem is used to test concyclicity of four points?

(A) Midpoint theorem
(B) Pythagoras theorem
(C) Opposite angles supplementary theorem
(D) Basic proportionality theorem

Correct Answer: C

Explanation:

A quadrilateral is cyclic if opposite angles are supplementary.

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Question (27)

QN009584

An exterior angle of a cyclic quadrilateral is equal to:

(A) Adjacent interior angle
(B) Opposite interior angle
(C) Half of adjacent angle
(D) Sum of interior angles

Correct Answer: B

Explanation:

Exterior angle equals the opposite interior angle.

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Question (28)

QN009585

If a quadrilateral has one pair of opposite angles supplementary, then it is:

(A) Cyclic
(B) Rhombus
(C) Parallelogram
(D) Trapezium

Correct Answer: A

Explanation:

Supplementary opposite angles imply cyclicity.

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Question (29)

QN009586

The sum of all interior angles of a cyclic quadrilateral is:

(A) 180°
(B) 270°
(C) 360°
(D) 540°

Correct Answer: C

Explanation:

Sum of interior angles of every quadrilateral is 360°.

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Question (30)

QN009587

In a cyclic quadrilateral, ∠A = 2x and ∠C = 4x. Find ∠A.

(A) 45°
(B) 60°
(C) 75°
(D) 90°

Correct Answer: B

Explanation:

2x+4x=180°, so x=30° and ∠A=60°.

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Question (21)

The vertices of a square are always:

Explanation:

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Question (22)

In cyclic quadrilateral PQRS, ∠P = 68°. Find ∠R.

Explanation:

Link:

Question (23)

A cyclic quadrilateral cannot have opposite angles:

Explanation:

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Question (24)

If four points are concyclic, then they lie on the:

Explanation:

Link:

Question (25)

In a cyclic quadrilateral, if ∠A = x° and ∠C = 2x°, then x equals:

Explanation:

Link:

Question (26)

Which theorem is used to test concyclicity of four points?

Explanation:

Link:

Question (27)

An exterior angle of a cyclic quadrilateral is equal to:

Explanation:

Link:

Question (28)

If a quadrilateral has one pair of opposite angles supplementary, then it is:

Explanation:

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Question (29)

The sum of all interior angles of a cyclic quadrilateral is:

Explanation:

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Question (30)

In a cyclic quadrilateral, ∠A = 2x and ∠C = 4x. Find ∠A.

Explanation:

Link:

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