Question

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

OR
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