In the following figure, if angles ∠ABC = 95° ∠EFD = 115° (not to scale). Then the angle ∠APC is equal to :
Answer & explanation
Correct answer: option 2
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 = 150o