Question

given m || n, find the value of x and y.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, \(2x + 7=3x - 15\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides: \(7=x - 15\). Then add 15 to both sides: \(x=22\).

Step3: Use linear - pair property

The angles \((y + 16)^{\circ}\) and \((3x - 15)^{\circ}\) form a linear - pair, so \((y + 16)+(3x - 15)=180\).

Step4: Substitute \(x = 22\) into the equation

\((y + 16)+(3\times22 - 15)=180\). First, calculate \(3\times22-15=66 - 15 = 51\). Then the equation becomes \(y + 16+51=180\), or \(y+67 = 180\). Subtract 67 from both sides to get \(y = 113\).

Answer:

\(x = 22\), \(y = 113\)