Question

use what you know about the interior angle measures of triangles to complete this problem. triangle pqr is an obtuse triangle, and the measure of angle q is 72°. what are possible measures of the other two angles? angle p angle r

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, if $\angle Q = 72^{\circ}$, then $\angle P+\angle R=180^{\circ}-\angle Q = 180 - 72=108^{\circ}$.

Step2: Consider the obtuse - angle condition

Since $\triangle PQR$ is an obtuse triangle, one of $\angle P$ or $\angle R$ must be greater than 90° and less than 180°. Let's assume $\angle P>90^{\circ}$. Then we can choose values such that $\angle P+\angle R = 108^{\circ}$. For example, if $\angle P = 100^{\circ}$, then $\angle R=108 - 100 = 8^{\circ}$.

Answer:

Angle $P = 100^{\circ}$, Angle $R = 8^{\circ}$ (There are multiple possible answers as long as one angle is obtuse and the sum of the two non - given angles is 108°)