Question

problem 5: 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. congruent c. unique d. supplementary e. a linear pair

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°.
Let the two acute angles be $\alpha$ and $\beta$. Then $\alpha+\beta + 90^{\circ}=180^{\circ}$.

Step2: Solve for the sum of acute angles

Subtract 90° from both sides of the equation: $\alpha+\beta=180^{\circ}-90^{\circ}=90^{\circ}$.
Two angles whose sum is 90° are complementary. So the acute angles of a right - triangle are complementary.

Answer:

A. complementary