Given: In ∆ABC,

AB=AC and ∠B=65°

To find : ∠A and ∠C

It is given that AB=AC and ∠B=65°

As two sides of the triangle are equal, we say that triangle is isosceles triangle, with vertex angle A.

Hence by the property of isosceles triangle we know that base angles are equal.

∴ ∠B = ∠C

∴∠C = ∠B =65°

Also, We know that,

Sum of all angles in any triangle = 180°

∴∠A + ∠B + ∠C = 180°

∠A + 65° + 65° = 180°

∠A + 130° = 180°

∴∠A = 180° - 130°

∠A = 50°

Hence, ∠C = 65° and ∠A = 50°