Question

15.
$(7y - 23)^{circ}$
$l$
$(23x - 16)^{circ}$
$(8x - 21)^{circ}$
$m$

Explanation:

Step1: Find the value of \(x\)

Since \(l\parallel m\), the sum of the interior angles on the same side of the transversal is \(180^{\circ}\).
So, \((23x - 16)+(8x - 21)=180\)
\(23x-16 + 8x-21=180\)
\(31x-37 = 180\)
\(31x=180 + 37\)
\(31x=217\)
\(x = 7\)

Step2: Find the value of \(y\)

Since \(l\parallel m\), the corresponding angles are equal.
The angle \((7y-23)^{\circ}\) and \((23x - 16)^{\circ}\) are corresponding angles.
Substitute \(x = 7\) into \(23x-16\), we get \(23\times7-16=161 - 16=145\)
So, \(7y-23=145\)
\(7y=145 + 23\)
\(7y=168\)
\(y = 24\)

Answer:

\(x = 7,y = 24\)