Question

what is the measure of $\angle prq$?
(image of triangle pqr with point n on a line extending from p, angle at n-p is 108°, angle at q is 62°, angle at r is ?. multiple choice options: 28°, 46°, 72°, 134°)

Explanation:

Step1: Find ∠QPR

Since ∠NPR and ∠QPR are supplementary (they form a linear pair), we use the formula \( \angle QPR = 180^\circ - \angle NPR \). Substituting \( \angle NPR = 108^\circ \), we get \( \angle QPR = 180^\circ - 108^\circ = 72^\circ \).

Step2: Find ∠PRQ

In triangle \( PQR \), the sum of interior angles is \( 180^\circ \). Let \( \angle PRQ = x \). We know \( \angle PQR = 62^\circ \) and \( \angle QPR = 72^\circ \). So, \( 62^\circ + 72^\circ + x = 180^\circ \). Solving for \( x \), we get \( x = 180^\circ - 62^\circ - 72^\circ = 46^\circ \).

Answer:

\( 46^\circ \) (corresponding to the option with \( 46^\circ \))