Question

giving reasons find the unknown angle

Answer 1

this question can be solved by exterior angle property also.
hope it will satisfy you

Answer 2

Let the triangle be ΔABC and m∠A = 70 and m∠B = m∠C = a.

Let D be a point on ray BC such that ∠ACD is exterior angle of ΔABC at point C.
Thus, according to question, m∠ACD = b.

Now, for ΔABC,
m∠A + m∠B + m∠C = 180
∴ 70 + a + a = 180
∴ 70 + 2a = 180
∴ 2a = 180 - 70
∴ 2a = 110
∴ a = 55

We know that measure of an exterior angle is the sum of measures of its interior opposite angles. 

In this case ∠ACD is exterior angle  and its interior opposite angles are ∠CAB and ∠ABC.

∴ m∠ACD = m∠CAB + m∠ABC
∴ b = 70 + a
∴ b = 70 + 55
∴ b = 125

Thus, a = 55° and b = 125°