Question

given ( m parallel n ), find the value of ( x ) and ( y ).

Explanation:

Step1: Use the property of supplementary angles

Since \(m\parallel n\), \((x - 14)^{\circ}\) and \((2x + 8)^{\circ}\) are same - side exterior and interior angles. They are supplementary. So, \((x-14)+(2x + 8)=180\).

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Step2: Use the property of vertical angles

\((7y-15)^{\circ}\) and \((2x + 8)^{\circ}\) are vertical angles. When \(x = 62\), \(2x+8=2\times62 + 8=124 + 8=132\). Then \(7y-15=132\).

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Answer:

\(x = 62\), \(y = 21\)