Question

1. find the values of x and y.

(x + 10)°
(18y + 5)°
(10x - 61)°

Explanation:

Step1: Assume vertical - angles are equal

Vertical - angles are equal. So, \(x + 10=10x - 61\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(10 = 9x-61\). Then add 61 to both sides: \(9x=71\), so \(x = 7\).

Step3: Assume adjacent - angles are supplementary

Adjacent angles are supplementary. Let's assume \((x + 10)+(18y + 5)=180\). Substitute \(x = 7\) into the equation: \((7 + 10)+(18y+5)=180\).

Step4: Simplify the equation

\(17+18y + 5=180\), which simplifies to \(18y+22 = 180\). Subtract 22 from both sides: \(18y=158\), then \(y=\frac{79}{9}\approx8.78\).

Answer:

\(x = 7\), \(y=\frac{79}{9}\)