Question

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

Explanation:

Step1: Find the value of \(x\)

Since \(m\parallel n\), the angles \((8x + 1)^{\circ}\) and \((9x-16)^{\circ}\) are supplementary.
So, \((8x + 1)+(9x-16)=180\)
\(8x+1 + 9x-16=180\)
\(17x-15 = 180\)
\(17x=180 + 15\)
\(17x=195\)
\(x = 17\)

Step2: Find the value of \(y\)

The angle \((8x + 1)^{\circ}\) and \((4y+3)^{\circ}\) are corresponding angles.
When \(x = 17\), \((8x + 1)=8\times17+1=137\)
Since \((8x + 1)=(4y+3)\)
\(137=4y + 3\)
\(4y=137-3\)
\(4y=134\)
\(y = 33.5\)

Answer:

\(x = 17\), \(y = 33.5\)