Question

In ΔABC, AB = AC and ∠A : ∠B = 4 : 3. Find the measure of ∠C.

Answer 1

We are given:

AB = AC triangle is isosceles ⇒ ∠B = ∠C

∠A : ∠B = 4 : 3

∠A = 4x

∠B = ∠C = 3x  ...(Since AB = AC, the base angles are equal)

Using the angle sum property of a triangle:

∠A + ∠B + ∠C = 180°

4x + 3x + 3x = 180°

⇒ 10x = 180°

⇒ x = 18°

Now,

∠A = 4x = 72°

∠B = ∠C = 3x = 54°