Question

triangle abc is a right triangle. what is the relationship between angles a and b? ○ they are congruent. ○ they are complementary. ○ they are supplementary. ○ there is no relationship between them. image of right triangle abc with right angle at c, angle at a labeled 59°, angle at b labeled 31°

Explanation:

Step1: Recall triangle angle sum

In a triangle, sum of angles is \(180^\circ\). For right triangle \(ABC\) (right at \(C\)), \(\angle C = 90^\circ\).

Step2: Calculate \(\angle A + \angle B\)

Let \(\angle A = 59^\circ\), \(\angle B = 31^\circ\). Then \(\angle A + \angle B = 59^\circ + 31^\circ = 90^\circ\).

Step3: Define complementary angles

Angles that add to \(90^\circ\) are complementary. So \(\angle A\) and \(\angle B\) are complementary.

Answer:

They are complementary.