Question

Find the value of a and b.

K
a=
b=
F
E
25°
A
B
b
D
C

Answer 1

a = 155°

b = 65°

Explanation:

Since FC ad ED are rays that intersect at point A

angles FAD, EAB and BCD are linear angles and their sum must equal 180°

⇒ m∠FAD + m∠EAB + m∠BCD = 180°

We have

m∠FAD = 25° (given)

m∠EAB = 90° (given)

m∠BCD = b

⇒ 25 + 90 + b = 180

⇒ 115 + b = 180

⇒ b = 180 - 115 = 65°

Again, since FC and ED are rays intersecting at point A

∠FAD = ∠EAC since they are vertically opposite angles

m∠FAD = a

m∠EAC = 90 + b = 90 + 65 = 155°

So a = 155°