If the angles A, B and C of Δ ABC satisfy the relation B – A = C – B, then find the measure of ∠B.

Question

If the angles A, B and C of &#x394; ABC satisfy the relation B &#x2013; A = C &#x2013; B , then find the measure of &#x2220; B.

Philoid · Accepted Answer

Given,

In ABC,

B - A = C - B

B + B = A + C

2B = A + C (i)

Now,

A + B + C = 180°

B = 180 - (A + C) (ii)

Using (i) in (ii), we get

B = 180 - 2B

3B = 180°

B = 60°