Question

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

Explanation:

Step1: Use the property of corresponding angles

Since \(m\parallel n\), \((6x - 16)^{\circ}=(3x + 17)^{\circ}\) (corresponding angles are equal).

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Step2: Use the property of linear - pair or vertical angles

First, find the measure of \((3x + 17)^{\circ}\). Substitute \(x = 11\) into \(3x+17\), we get \(3\times11+17=33 + 17=50^{\circ}\).
Since \((3x + 17)^{\circ}\) and \((2y + 14)^{\circ}\) are supplementary (linear - pair of angles, because they form a straight line along the transversal), \((3x + 17)+(2y + 14)=180\).
Substitute \(x = 11\) into the equation: \(50+(2y + 14)=180\).

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Answer:

\(x = 11\) and \(y = 58\)