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.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In right - triangle ABC, ∠C = 90°. Let ∠A and ∠B be the other two angles. So, ∠A+∠B + ∠C=180°.

Step2: Substitute the value of ∠C

Since ∠C = 90°, we have ∠A+∠B+90° = 180°.

Step3: Solve for ∠A + ∠B

Subtract 90° from both sides of the equation: ∠A+∠B=180° - 90°=90°.

Step4: Recall the definition of complementary angles

Two angles are complementary if their sum is 90°. Since ∠A + ∠B = 90°, angles A and B are complementary.

Answer:

They are complementary.