Question

If two angles of a triangle have equal measures, and the third angle measures 90°, what are the angle measures of the triangle?

A) 60°, 60°, 60°
B) 45°, 90°, 90°
C) 30°, 30°, 90°
D) 45°, 45°, 90°

Answer 1

In a triangle, if two angles have equal measures and one angle is 90°, the angle measures of the triangle are 45°, 45°, and 90°. The correct answer is option D.

Step-by-step explanation:

In a triangle, the sum of the angles is always 180°. If two angles of a triangle have equal measures and one angle is 90°, we can find the measure of the other two angles.

Let's say the two angles with equal measures are x degrees each. Since the sum of all three angles is 180°, we can set up the equation

x + x + 90 = 180.

Simplifying the equation, we get 2x + 90 = 180. Subtracting 90 from both sides, we find 2x = 90.

Dividing both sides by 2, we get x = 45.

So, the angle measures of the triangle are 45°, 45°, and 90°.

Therefore, the correct answer is D) 45°, 45°, 90°.