Question

14.m∠pxq=(8x - 3)°, m∠pxs=(10x + 30)°. find the value of x and m∠qxs.

Explanation:

Step1: Set up equation

Since $\angle PXQ$ and $\angle PXS$ are supplementary (linear - pair of angles), their sum is $180^{\circ}$. So, $(8x - 3)+(10x + 30)=180$.

Step2: Combine like - terms

$8x+10x-3 + 30=180$, which simplifies to $18x+27 = 180$.

Step3: Isolate the variable term

Subtract 27 from both sides: $18x=180 - 27$, so $18x=153$.

Step4: Solve for x

Divide both sides by 18: $x=\frac{153}{18}=\frac{17}{2}=8.5$.

Step5: Find $m\angle QXS$

First, find $m\angle PXQ$ and $m\angle PXS$. $m\angle PXQ=8x - 3=8\times8.5-3=68 - 3 = 65^{\circ}$, $m\angle PXS=10x + 30=10\times8.5+30=85 + 30 = 115^{\circ}$. Since $\angle QXS=\angle PXS-\angle PXQ$, $m\angle QXS=115 - 65=50^{\circ}$.

Answer:

$x = 8.5$
$m\angle QXS = 50^{\circ}$