Question

in the figure below, ( m angle pqs = 112^circ ).
(a) write an equation to find ( x ). make sure you use an \=\ sign in your answer.
equation:
(b) solve for ( x ).
( x = )

Explanation:

Part (a)

Step1: Analyze angle composition

The angle \( \angle PQS \) is composed of \( \angle PQR \) (which is \( 3x^\circ \)) and \( \angle RQS \) (which is \( 52^\circ \)). So the sum of these two angles equals \( \angle PQS \).
\( 3x + 52 = 112 \)

Part (b)

Step1: Subtract 52 from both sides

To isolate the term with \( x \), we subtract 52 from both sides of the equation \( 3x + 52 = 112 \).
\( 3x + 52 - 52 = 112 - 52 \)
\( 3x = 60 \)

Step2: Divide by 3

Divide both sides by 3 to solve for \( x \).
\( \frac{3x}{3} = \frac{60}{3} \)
\( x = 20 \)

Answer:

s:
(a) Equation: \( 3x + 52 = 112 \)
(b) \( x = 20 \)