Triangle abc is an isosceles right triangle. what is the measure of a base angle

The measure of the base angle = 45°

Step-by-step explanation:

For better explanation of the solution see the attached figure of the diagram :

Given : An isosceles right triangle ABC

To find : Measure of the base angle

Solution :

Since, The triangle is right angle triangle.

⇒ m∠B = 90°

Also, ΔABC is an isosceles triangle

So, AB = BC

Now, Angles opposite to equal sides are equal

⇒ m∠A = m∠C

Now, Using Angles sum property of a triangle

⇒ m∠A + m∠B + m∠C = 180°

⇒ m∠C + 90° + m∠C = 180°

⇒ 2m∠C = 180° - 90°

⇒ 2m∠C = 90°

⇒ m∠C = 45°

Hence, The measure of the base angle = 45°