Question

16 multiple choice 6 points
what is the value of x?
$x=23$
$x=35$
$x=58$
$x=93$

Explanation:

Step1: Find ∠SQR in △SQR

First, calculate the interior angle at Q in △SQR. The sum of angles in a triangle is $180^\circ$.
$\angle SQR = 180^\circ - 35^\circ - 58^\circ = 87^\circ$

Step2: Calculate x using linear pair

∠PQS ($x^\circ$) and ∠SQR are a linear pair, so their sum is $180^\circ$.
$x = 180^\circ - 87^\circ = 93^\circ$

Answer:

x = 93