Question

Find the measure of A as indicates in the picture.

In case the picture blurs
Top angle = x + 63
Left angle = x + 96
Right angle = x + 149

Answer 1

m∠A = 58°

Explanation:

In ΔABC,

m∠BAC = (x + 63)°

m∠ABC = (x + 96)° [Vertically opposite angles]

m∠ACB = (180° - 149°)

= 31°

By triangle sum theorem,

m∠ABC + m∠ACB + m∠BAC = 180°

(x + 96) + 31 + (x + 63) = 180°

2x + 190 = 180

2x = -10

x = -5

Therefore, measure angle A = (x + 63)

= -5 + 63

= 58°