Question

use this figure to answer the question below.
what is the measure of \\( \angle psq \\)?
label optional

Explanation:

Step1: Find the value of \( x \)

Since \( \angle PSR = 90^{\circ} \), we have \( (3x + 10)+(3x + 2)=90 \).
Combine like - terms: \( 6x+12 = 90 \).
Subtract 12 from both sides: \( 6x=90 - 12=78 \).
Divide both sides by 6: \( x=\frac{78}{6}=13 \).

Step2: Calculate the measure of \( \angle PSQ \)

Substitute \( x = 13 \) into the expression for \( \angle PSQ\) (\(3x + 10\)).
\(3x+10=3\times13 + 10\).
First, multiply: \(3\times13 = 39\).
Then, add: \(39+10=55\).

Answer:

\( 55^{\circ} \)