In a cyclic quadrilateral ABCD, the angle A is 100°. What is the measure of the angle C?

Question

In a cyclic quadrilateral ABCD, the angle A is 100°. What is the measure of the angle C?

1. A. 70°
2. B. 80° (Correct answer)
3. C. 90°
4. D. 110°

Correct Answer

Option B — 80°

Detailed Solution & Explanation

The correct answer is 80°.

Key Points

• In a cyclic quadrilateral — one whose four vertices lie on a circle — the opposite angles are supplementary, summing to 180°.
• A and C are opposite, so:
  • ∠C = 180° − 100° = 80°
• The same holds for B and D, which must also sum to 180°.

Additional Information

• The converse is equally useful: if a quadrilateral's opposite angles sum to 180°, the quadrilateral is cyclic.
• An exterior angle of a cyclic quadrilateral equals the interior opposite angle, a result that shortens many circle problems.
• Related circle theorems: the angle at the centre is twice the angle at the circumference on the same arc; angles in the same segment are equal; and the angle in a semicircle is a right angle.

प्रश्न (हिन्दी में)

एक चक्रीय चतुर्भुज ABCD में, कोण A 100° है। कोण C का माप क्या है?

1. A. 70°
2. B. 80°
3. C. 90°
4. D. 110°