Question

Quadrilateral 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) which is the angle inscribed in the arc BCD?

Answer 1

(1) arc CBA intercepted by ∠D.
(2) If m∠B = 65°, m∠D=180-65=115
(3) If m∠a = 125°, ∠C=180-125=55
(4) angle inscribed in the arc BCD=angle A

Answer 2

Answer:

m∠D = 115°

m∠C = 55°

Step-by-step explanation:

Quadrilateral ABCD is a cyclic quadrilateral. Answer the following questions.

If m∠B = 65°, what is the measure of m∠D?

If m∠a = 125°, what is the measure of ∠C?

In a cyclic quadrilateral Sum of opposite angles = 180°

∠A & ∠C are opposite angles

∠B & ∠D are also opposite angles

m∠B +  m∠D  = 180°

=> 65° +  m∠D  = 180°

=> m∠D = 115°

m∠A +  m∠C  = 180°

=> 125° +  m∠C  = 180°

=> m∠C = 55°