Question

1. find the values of x and y.

Explanation:

Step1: Find the value of \(x\)

Vertical angles are equal. So \(3x - 11+5x - 17 = 180\) (since they form a linear - pair).
Combine like terms: \(8x-28 = 180\).
Add \(28\) to both sides: \(8x=180 + 28=208\).
Divide both sides by \(8\): \(x=\frac{208}{8}=26\).

Step2: Find the value of \(y\)

The angle \((2y + 5)\) and the right - angle (\(90^{\circ}\)) are complementary (assuming the geometric relationship from the figure). So \(2y+5=90\).
Subtract \(5\) from both sides: \(2y=90 - 5 = 85\).
Divide both sides by \(2\): \(y=\frac{85}{2}=42.5\).

Answer:

\(x = 26\) and \(y = 42.5\)