If triangle abc is isosceles, what is the value of & angle; a?

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∠A = 78°

Explanation:
We are given that ΔABC is isosceles-angled triangle.
This means that:
AB = AC
∠ABC = ∠ACB 
We are given that ∠ABC = 51°
This means that ∠ACB = 51°

Now, the sum of measures of the angles of a triangle = 180°
This means that:
∠A + ∠ABC + ∠ACB = 180
∠A + 51 + 51 = 180
∠A + 102 = 180
∠A = 180 - 102 
∠A = 78°

Hope this helps :)