Question

find the values of x and y.
(13x)°
38°
x =
y =

Explanation:

Step1: Use the fact that vertical - angles are equal

Since $\angle BGC$ and $\angle FGD$ are vertical - angles, and $\angle BGD = 90^{\circ}$, we know that $13x+38 = 90$.

Step2: Solve the equation for x

Subtract 38 from both sides of the equation $13x+38 = 90$:
$13x=90 - 38$
$13x = 52$
Divide both sides by 13: $x=\frac{52}{13}=4$.

Step3: Use the fact that vertical - angles are equal for y

Since $\angle FGD$ and $\angle CGE$ are vertical - angles, $y = 38$.

Answer:

$x = 4$
$y = 38$