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Question (11)

QN009568

Which of the following quadrilaterals is always cyclic?

(A) Kite
(B) Rectangle
(C) Parallelogram
(D) Rhombus

Correct Answer: B

Explanation:

Opposite angles of a rectangle are supplementary.

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Question (12)

QN009569

In a cyclic quadrilateral, the sum of one pair of opposite angles is:

(A) 90°
(B) 120°
(C) 180°
(D) 360°

Correct Answer: C

Explanation:

Opposite angles of a cyclic quadrilateral add up to 180°.

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Question (13)

QN009570

If the exterior angle of a cyclic quadrilateral is 105°, then the interior opposite angle is:

(A) 75°
(B) 85°
(C) 95°
(D) 105°

Correct Answer: D

Explanation:

Exterior angle equals the opposite interior angle.

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Question (14)

QN009571

Which figure can always be inscribed in a circle?

(A) Rectangle
(B) General parallelogram
(C) Rhombus
(D) Trapezium

Correct Answer: A

Explanation:

Every rectangle is cyclic.

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Question (15)

QN009572

In a cyclic quadrilateral ABCD, ∠A : ∠C = 4 : 5. Find ∠A.

(A) 60°
(B) 70°
(C) 80°
(D) 90°

Correct Answer: C

Explanation:

Let angles be 4x and 5x. Then 9x=180°, x=20°, so ∠A=80°.

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Question (16)

QN009573

If opposite angles of a quadrilateral are supplementary, then the quadrilateral is:

(A) A parallelogram
(B) Cyclic
(C) A trapezium
(D) A rhombus

Correct Answer: B

Explanation:

Supplementary opposite angles imply cyclicity.

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Question (17)

QN009574

In a cyclic quadrilateral, if one exterior angle is 125°, then the opposite interior angle is:

(A) 55°
(B) 65°
(C) 125°
(D) 145°

Correct Answer: C

Explanation:

Exterior angle equals the opposite interior angle.

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Question (18)

QN009575

Which of the following is not always cyclic?

(A) Square
(B) Rectangle
(C) Isosceles trapezium
(D) Rhombus

Correct Answer: D

Explanation:

A rhombus is cyclic only when it is a square.

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Question (19)

QN009576

In a cyclic quadrilateral, opposite angles are:

(A) Equal
(B) Supplementary
(C) Complementary
(D) Reflex

Correct Answer: B

Explanation:

Opposite angles of a cyclic quadrilateral are supplementary.

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Question (20)

QN009577

A quadrilateral has opposite angles 100° and 80°. The quadrilateral is:

(A) Cyclic
(B) Non-cyclic
(C) A square
(D) A kite

Correct Answer: A

Explanation:

Since 100°+80°=180°, the quadrilateral is cyclic.

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Question (11)

Which of the following quadrilaterals is always cyclic?

Explanation:

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Question (12)

In a cyclic quadrilateral, the sum of one pair of opposite angles is:

Explanation:

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Question (13)

If the exterior angle of a cyclic quadrilateral is 105°, then the interior opposite angle is:

Explanation:

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Question (14)

Which figure can always be inscribed in a circle?

Explanation:

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Question (15)

In a cyclic quadrilateral ABCD, ∠A : ∠C = 4 : 5. Find ∠A.

Explanation:

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Question (16)

If opposite angles of a quadrilateral are supplementary, then the quadrilateral is:

Explanation:

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Question (17)

In a cyclic quadrilateral, if one exterior angle is 125°, then the opposite interior angle is:

Explanation:

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Question (18)

Which of the following is not always cyclic?

Explanation:

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Question (19)

In a cyclic quadrilateral, opposite angles are:

Explanation:

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Question (20)

A quadrilateral has opposite angles 100° and 80°. The quadrilateral is:

Explanation:

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