Question

Determine the measure of each of the equal angles of a right-angled isosceles triangle.

ABC is a right-angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.

Answer 1

Given to determine the measure of each of the equal angles of right– angled isosceles triangle

Consider on a right – angled isosceles triangle ABC such that

∠A = 90° and AB = AC

Since, AB = AC ⇒ ∠C = ∠B   ……….(1)

[Angles opposite to equal sides are equal] Now,

Sum of angles in a triangle = 180°

∠A + ∠B +∠C = 180°

⇒  90° + ∠B + ∠B = 180°       [ ∴∠A = 90° and ∠B = ∠C ]  

⇒ 2∠B = 90°

⇒ ∠B = 45°⇒  ∠C = 45°

∴ ∠B =∠C = 45°

Hence, the measure of each of the equal angles of a right-angled isosceles triangle is 45°.