In the following g figures, if angles ∠ABC = 95ᵒ ∠FED = 115ᵒ (not to scale). Then the angle ∠APC is equal to: [Image]

In the following g figures, if angles ∠ABC = 95ᵒ ∠FED =…

In the following g figures, if angles ∠ABC = 95^o ∠FED = 115^o (not to scale). Then the angle ∠APC is equal to:

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e 150^o

Understanding

Application

The opposite angle of the cycle quadrilateral is 180°.

We will join points A & F.

In Quadrilateral AFED

⇒ ∠ABC + ∠AFC = 180^o

⇒ 95^o + ∠AFC = 180^o

^⇒∠AFC = 85^o

In Quadrilateral ABCF

⇒ ∠ABC + ∠AFC = 180^o

⇒ 95^o + ∠AFC = 180^o

⇒ ∠AFC = 85^o

In triangle AFP

⇒ 85^o + 65^o + ∠FPA = 180^o

⇒ ∠FPA = 180^o - 150^o

⇒ ∠FPA = 30^o

⇒ ∠APC + ∠FPA = 180^o

⇒ ∠APC = 150^o