Question

solve for x and y.

x = 110
y = 28

Explanation:

Step1: Use the property of supplementary angles

When two parallel lines are cut by a transversal, consecutive - interior angles are supplementary. The angle of \(100^{\circ}\) and \((x - 10)^{\circ}\) are supplementary. So, \(100+(x - 10)=180\).
Simplify the left - hand side of the equation: \(100+x-10 = 180\), which gives \(x+90 = 180\).
Subtract 90 from both sides: \(x=180 - 90\), so \(x = 90+20=110\).

Step2: Use the property of vertical angles

The angle \((x - 10)^{\circ}\) and \((2y + 24)^{\circ}\) are vertical angles. Since \(x = 110\), then \((x - 10)=(110 - 10)=100^{\circ}\). So, \(2y+24 = 100\).
Subtract 24 from both sides: \(2y=100 - 24\), which gives \(2y = 76\).
Divide both sides by 2: \(y=\frac{76}{2}=28\).

Answer:

\(x = 110\), \(y = 28\)