Triangle ABC is an isosceles right triangle. What is the measure of one base angle? 
30°, 45°, 60°, 90°

Solution:

Given that triangle, ABC is an isosceles right triangle

Clearly, by given data, we can say that angle B is 90°

By the angle sum property of an isosceles triangle, we know that the sum of all angles of a triangle is equal to 180°.

Let ∠A + ∠B + ∠C =180°

We know ∠B = 90°

∠A + ∠C + 90 = 180°

∠A + ∠C = 180° - 90° = 90°

Another property of isosceles triangle states that an isosceles triangle therefore has both two equal sides and two equal angles

Let ∠A = ∠C = x

⇒ x + x = 90°

⇒ 2x = 90°

⇒ x = 45°

Therefore, the base angle ∠C = 45°

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Triangle ABC is an isosceles right triangle. What is the measure of one base angle? 

 Summary:

If triangle ABC is an isosceles right triangle then the measure of one base angle is 45°.