Question

given (mparallel n), find the value of (x) and (y). (7y - 15)° (x - 14)° m (2x + 8)° n

Explanation:

Step1: Use corresponding - angles property

Since \(m\parallel n\), the corresponding angles are equal. So, \(x - 14=2x + 8\).
Solve the equation \(x - 14=2x + 8\) for \(x\):
Subtract \(x\) from both sides: \(-14=x + 8\).
Then subtract 8 from both sides: \(x=-22\).

Step2: Use linear - pair property

The angles \((7y - 15)^{\circ}\) and \((x - 14)^{\circ}\) form a linear - pair, so \((7y-15)+(x - 14)=180\).
Substitute \(x = - 22\) into the equation:
\(7y-15+(-22 - 14)=180\).
\(7y-15-36 = 180\).
\(7y-51 = 180\).
Add 51 to both sides: \(7y=180 + 51=231\).
Divide both sides by 7: \(y = 33\).

Answer:

\(x=-22,y = 33\)