Question

select the correct answer. in the figure, angle a measures 41° and angle d measures 32°. what is the measurement of angle e? a. 88° b. 90° c. 95° d. 100°

Explanation:

Step1: Find angle C in triangle ABC.

In right - triangle ABC, $\angle A = 41^{\circ}$ and $\angle B=90^{\circ}$. Using the angle - sum property of a triangle ($\angle A+\angle B+\angle C = 180^{\circ}$), we get $\angle C=180^{\circ}-90^{\circ}-41^{\circ}=49^{\circ}$.

Step2: Find angle E.

In triangle CDE, $\angle C = 49^{\circ}$ and $\angle D = 32^{\circ}$. Using the angle - sum property of a triangle ($\angle C+\angle D+\angle E = 180^{\circ}$), we have $\angle E=180^{\circ}-49^{\circ}-32^{\circ}=99^{\circ}$.

Answer:

C. $99^{\circ}$