Question

triangle abc is a right triangle. what is the relationship between angles a and b? \bigcirc they are congruent. \bigcirc they are complementary. \bigcirc they are supplementary. \bigcirc there is no relationship between them.

Explanation:

In a right triangle, the sum of the two non - right angles is \(90^{\circ}\) (since the sum of all angles in a triangle is \(180^{\circ}\) and one angle is \(90^{\circ}\)). Angles A and B are the non - right angles. If we add their measures (\(59^{\circ}+31^{\circ} = 90^{\circ}\)), two angles whose sum is \(90^{\circ}\) are complementary. Congruent angles have the same measure, and these two angles have different measures. Supplementary angles have a sum of \(180^{\circ}\), which is not the case here. And there is a clear relationship (their sum is \(90^{\circ}\)) between them.

Answer:

They are complementary.