Question

using algebra

1. if $m\angle pqt = (3x + 47)^\circ$ and $m\angle sqr = (6x - 25)^\circ$, find the measure of $\angle sqr$.

image of two intersecting lines with points p, t on one line and s, r on the other, intersecting at q. angles at q: $\angle pqt$ is labeled $3x + 47$ and $\angle sqr$ is labeled $6x - 25$

Explanation:

Step1: Identify vertical angles

$\angle PQT$ and $\angle SQR$ are vertical angles, so they are equal. Thus, $3x + 47 = 6x - 25$.

Step2: Solve for x

Subtract $3x$ from both sides: $47 = 3x - 25$.
Add 25 to both sides: $72 = 3x$.
Divide by 3: $x = 24$.

Step3: Find $m\angle SQR$

Substitute $x = 24$ into $6x - 25$: $6(24) - 25 = 144 - 25 = 119$.

Answer:

The measure of $\angle SQR$ is $119^\circ$.