Question

complete this sentence with the best of the choices given. the acute angles of a right triangle are _________. after you pick your answer press go. a. complementary b. adjacent c. supplementary d. a linear pair e. congruent

Explanation:

Step1: Recall triangle - angle sum property

The sum of the interior angles of a triangle is 180°. In a right - triangle, one angle is 90°.

Step2: Let the acute angles be $\alpha$ and $\beta$

We have $\alpha+\beta + 90^{\circ}=180^{\circ}$.

Step3: Solve for $\alpha+\beta$

Subtract 90° from both sides of the equation: $\alpha+\beta=180^{\circ}-90^{\circ}=90^{\circ}$.

Step4: Recall angle relationship definitions

Two angles whose sum is 90° are called complementary angles. So the acute angles of a right - triangle are complementary.

Answer:

A. complementary