Question

□ABCD is a cyclic quadrilateral. Answer the following questions:


(1) Name the arc intercepted by ∠D.
(2) If m∠B = 65°, what is the measure of m∠D?
(3) If m∠A = 125°, what is the measure of ∠C?
(4) What is angle inscribed in the arc BCD?

Answer 1

The given figure is a cyclic quadrilateral.

(1) The arc intercepted by ∠D = arc ABC.

(2) m∠B = 65°
But m∠B+ m∠D = 180° (Sum of opposite angles of a cyclic quadrilateral is 180°)
⇒ m∠D = 180° − 65°
⇒ m∠D = 115°
∴ The measure of ∠D = 115°

(3) m∠A = 125°
But m∠A+ m∠C = 180° (Sum of opposite angles of a cyclic quadrilateral is 180°)
⇒ m∠A = 180° − 125°
⇒ m∠A = 55°
∴ The measure of ∠A = 55°

(4) The angle inscribed in the arc BCD is ∠C .