Question

find the measure of ∠psr.
(131 - 2x)°
(6x + 67)°
m∠psr = □°
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transversals of parallel lines: find angle measures (81)
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lesson: transversals of parallel lines

Explanation:

Step1: Identify angle - relationship

Angles $\angle PSR$ and $\angle ORS$ are alternate - interior angles. Since the lines are parallel, they are equal. So, $131 - 2x=6x + 67$.

Step2: Solve the equation for x

First, add $2x$ to both sides: $131=6x + 2x+67$, which simplifies to $131 = 8x+67$. Then subtract 67 from both sides: $131 - 67=8x$, so $64 = 8x$. Divide both sides by 8: $x=\frac{64}{8}=8$.

Step3: Find the measure of $\angle PSR$

Substitute $x = 8$ into the expression for $\angle PSR$: $m\angle PSR=131-2x$. So, $m\angle PSR=131-2\times8=131 - 16 = 115$.

Answer:

$115$