Question

find m∠q in parallelogram pqrs.
p
2x - 69°
q
s
3x - 56°
r
m∠q = □°

Explanation:

Step1: Recall property of parallelogram

In a parallelogram, adjacent - angles are supplementary, so $\angle P+\angle S = 180^{\circ}$.
$(2x - 69)+(3x - 56)=180$

Step2: Combine like - terms

$2x+3x-69 - 56 = 180$
$5x-125 = 180$

Step3: Solve for $x$

Add 125 to both sides: $5x=180 + 125$
$5x=305$
Divide both sides by 5: $x=\frac{305}{5}=61$

Step4: Find $\angle Q$

Since $\angle Q$ and $\angle S$ are adjacent angles in a parallelogram, $\angle Q+\angle S = 180^{\circ}$. First, find $\angle S$: $\angle S=3x - 56$. Substitute $x = 61$ into the formula for $\angle S$: $\angle S=3\times61-56=183 - 56 = 127^{\circ}$. Then $\angle Q=180-\angle S$. So $\angle Q = 180 - 127=53^{\circ}$

Answer:

$53$