In the following figure, if angles ∠ABC = 95° ∠EFD = 115° (not to scale). Then the angle ∠APC is equal to :

150°

We have,

∠ABC = 95° and ∠FED = 115°

We know that,

The sum of the opposite angle of cycle quadrilateral is 180°.

Construction = Join A to F

In quadrilateral ABCF

∠ABC + ∠AFC = 180

= 95 + ∠AFC = 180

= ∠AFC = 180 - 95

= ∠AFC = 85

In quadrilateral AFED

∠FAD + ∠FED = 180

= ∠FAD + 115 = 180

= ∠FAD = 180 - 115

= ∠FAD = 65

In ΔAFP

= ∠AFP + ∠FAP + ∠FPA = 180

= 85 + 65 + ∠FPA = 180

= ∠FPA = 180 - 150

= ∠FPA = 30

We know that,

∠APC + ∠FPA = 180

= ∠APC + 30 = 180

= ∠APC = 180 - 30

∠APC = 150^o