Question

what are the measures of the angles in an isosceles right triangle?
a. 45°, 45°, and 90°
b. 30°, 60°, and 90°
c. cannot be determined
d. 60°, 60°, and 90°

Explanation:

Step1: Recall triangle - angle sum

The sum of the interior angles of a triangle is 180°.

Step2: Identify right - angle measure

In a right - triangle, one angle is 90°.

Step3: Use isosceles property

In an isosceles triangle, two angles are equal. Let the measure of each of the equal angles be \(x\). Then \(x + x+90^{\circ}=180^{\circ}\).

Step4: Solve for \(x\)

Combining like terms gives \(2x=180^{\circ}- 90^{\circ}=90^{\circ}\). Dividing both sides by 2, we get \(x = 45^{\circ}\).

Answer:

A. 45°, 45°, and 90°