Question

find the measure of acute angle of a right angled isosceles triangle

Answer 1

Since, the triangle is isosceles

Its both angles other than right angle are equal.


Let each of equal angles be a

By angle sum property of triangle,

a + a + 90 = 180

=> 2a = 90

=> a = 45

Measure of each acute angle = 45°

Answer 2

Here is your solution

Given :-

ABC is a right isosceles Triangle .

in which

Two sides are equal

I. e

AC = BC
hence
∠A=∠B

∠ACB = 90°

we know that

sum of triangle is 180°

∠A+∠B+∠c = 180

∠A+∠B+90° = 180

∠A+∠A+90° = 180° [ ∠A = ∠B Given ]

2∠A+90° = 180°

2∠A = 180°-90°

∠A = 90°/2

∠A=45°

Hence

measure of acute angle of a right angled isosceles triangle is 45°

Hope it helps you