Question

what is the value of x? art not to scale.
○ x=23
○ x=35
○ x=58
○ x=93

Explanation:

Step1: Find the third angle in triangle SQR

In triangle \( SQR \), the sum of interior angles is \( 180^\circ \). We know two angles: \( \angle S = 35^\circ \) and \( \angle R = 58^\circ \). Let \( \angle SQR = y \). Then:
\[
y + 35^\circ + 58^\circ = 180^\circ
\]
\[
y = 180^\circ - 35^\circ - 58^\circ
\]
\[
y = 87^\circ
\]

Step2: Use linear pair to find \( x \)

Angles \( x \) and \( y \) form a linear pair (they are adjacent and supplementary), so:
\[
x + y = 180^\circ
\]
Substitute \( y = 87^\circ \):
\[
x = 180^\circ - 87^\circ
\]
Wait, that's not matching the options. Wait, maybe I made a mistake. Wait, no, wait: Wait, the triangle angle sum: \( 35 + 58 = 93 \), so the third angle (at Q in the triangle) is \( 180 - 93 = 87 \)? No, wait, no, the exterior angle theorem: the exterior angle \( x \) is equal to the sum of the two non-adjacent interior angles. Oh! Right, exterior angle theorem. So \( x = 35^\circ + 58^\circ \).
\[
x = 35 + 58
\]
\[
x = 93
\]

Answer:

\( x = 93 \) (corresponding to the option \( x = 93 \))