Question

Two circles intersect in A and B. P, A, E are collinear
points. C, B, D are collinear points PCDE is a quadrilateral.
If angle CPE = 95°. Identify the value of angle PED.
95°
C
(A) 65°
(B) 105° (C) 95°
4D) 85°​

Answer 1

The value of ∠PED = 85°.

Step-by-step explanation:

In the given cyclic quadrilateral PABC,

∠APC+∠ABC= 180° [Sum of opposite anlge of a cyclic quadrilateral is 180°]

95°+∠ABC = 180°

∠ABC = 180°-95°

          = 85°

Also,In a cyclic quadrilateral AEDB,∠ABC is the exterior angle.

We know that,In a cyclic quadrilateral Exterior angle is equal to opposite interior angle.

So,∠ABC = ∠AED

⇒∠AED = 85°

or ∠PED = 85°

Hence,the value of ∠PED = 85°.