Question

find the value of each variable.
2(5x - 5)°
(5y + 5)° (3x - 5)°
20y°
x =
y =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $2(5x - 5)=3x - 5$.
First, expand the left - hand side: $10x-10 = 3x - 5$.

Step2: Solve for x

Subtract $3x$ from both sides: $10x-3x - 10=3x-3x - 5$, which simplifies to $7x-10=-5$.
Then add 10 to both sides: $7x-10 + 10=-5 + 10$, so $7x = 5$.
Divide both sides by 7: $x=\frac{5}{7}$.

Step3: Use linear - pair property

$(5y + 5)+20y=180$ (since they form a linear pair).
Combine like terms: $5y+20y + 5=180$, so $25y+5 = 180$.

Step4: Solve for y

Subtract 5 from both sides: $25y+5 - 5=180 - 5$, which gives $25y=175$.
Divide both sides by 25: $y = 7$.

Answer:

$x=\frac{5}{7}$, $y = 7$