Question

In ΔABC, AB = BC and ∠B = 64°. Find ∠C.

Answer 1

Answer

Given,

AB = BC

Hence,

∠B = ∠C

So,

∠C => 64°

Also,

∠A+ ∠B+ ∠C = 180°

∠A+64+64 = 180

∠A = 180-128

∠A = 52°

Answer 2

Answer:    58°

Step-by-step explanation:

[The figure is in the attachment below]

In triangle ABC ,

AB = BC     (given)

=> triangle ABC is an isoceles triangle (two sides are equal)

Given angle B = 64°

angle A = angle C    

(angles opposite to equal sides in an isoceles triangle are equal)

Now,

angle A + angle B + angle C = 180°  (sum of angles of a triangle = 180°)

angle C + 64° + angle C = 180°  (substituting angle B and angle A)

2(angle C) + 64° = 180°

2(angle C) = 180°-64° = 116°

angle C = 116°÷2 = 58 °