Question

find the values of x and y.
(2x + 3)°
52°
(5y)°
127°
x =
y =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle AGB$ and $\angle DGE$ are vertical angles. So, $2x + 3=52$.

Step2: Solve for x

Subtract 3 from both sides of the equation $2x+3 = 52$: $2x=52 - 3=49$. Then divide both sides by 2: $x=\frac{49}{2}=24.5$.

Step3: Use the fact that $\angle FGE$ and the $127^{\circ}$ angle are supplementary

Supplementary angles add up to $180^{\circ}$. So, $5y+127 = 180$.

Step4: Solve for y

Subtract 127 from both sides of the equation $5y + 127=180$: $5y=180 - 127 = 53$. Then divide both sides by 5: $y=\frac{53}{5}=10.6$.

Answer:

$x = 24.5$
$y = 10.6$