Question

what is a measure of $angle pqr$?
$\bigcirc$ $23^circ$
$\bigcirc$ $36^circ$
$\bigcirc$ $42^circ$
$\bigcirc$ $47^circ$

Explanation:

Step1: Use exterior angle property

The exterior angle of a triangle equals the sum of the two non-adjacent interior angles. For $\triangle PQR$, $\angle SPQ$ is an exterior angle, so:
$\angle SPQ = \angle PQR + \angle PRQ$

Step2: Rearrange to solve for $x$

Substitute the known angle values ($\angle SPQ=35^\circ$, $\angle PRQ=12^\circ$, $\angle PQR=x^\circ$):
$x = 35^\circ - 12^\circ$

Step3: Calculate the value

$x = 23^\circ$

Answer:

23°