Question

find the values of x and y.

x =

y =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle NTQ$ and $\angle STR$ are vertical angles. So, $13y = 52$.

Step2: Solve for $y$

Divide both sides of the equation $13y = 52$ by 13: $y=\frac{52}{13}=4$.

Step3: Use complementary - angle property

$\angle QTR$ is a right - angle ($90^{\circ}$). So, $2x+13y = 90$.

Step4: Substitute $y = 4$ into the equation

Substitute $y = 4$ into $2x+13y = 90$, we get $2x+13\times4 = 90$.

Step5: Simplify the equation

$2x + 52=90$.

Step6: Solve for $x$

Subtract 52 from both sides: $2x=90 - 52=38$. Then divide both sides by 2: $x = 19$.

Answer:

$x = 19$
$y = 4$