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

The correct answer to the student's question is D) 45°, 45°, 90°, which are the angle measures of a right isosceles triangle.

Step-by-step explanation:

If two angles of a triangle have equal measures and the third angle measures 90°, the triangle is known as a right isosceles triangle. This means one angle is a right angle (90°) and the other two angles must be equal because triangles always have a total of 180°.

To find the measure of the remaining two angles, we subtract the right angle from the total sum of the triangle's angles: 180° - 90° = 90°. Then divide this number by two because the two remaining angles are equal, giving us 90° / 2 = 45° for each angle.

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