Question

In triangle ABC, AB is congruent to CA. Given that measure of ∠A = 54°, find measure of ∠C.

Answer 1

The measure of ∠C in triangle ABC, where ∠A = 54° and the triangle is isosceles, is 72°.

Step-by-step explanation:

Since triangle ABC has two congruent sides (AB congruent to CA), it is an isosceles triangle. The two base angles in an isosceles triangle are congruent, which means the measure of ∠B is also 54°. The sum of all angles in any triangle is 180°. Therefore, to find the measure of ∠C, we subtract the measures of ∠A and ∠B from 180°.

Measure of ∠C = 180° - Measure of ∠A - Measure of ∠B
Measure of ∠C = 180° - 54° - 54°
Measure of ∠C = 180° - 108°
Measure of ∠C = 72°

The measure of ∠C in triangle ABC, where ∠A = 54° and the triangle is isosceles, is 72°.