Question

find the values of x and y.

x=

y=

Explanation:

Step1: Find the value of \(x\)

Vertical angles are equal. So, \(5x + 4=114\).
Subtract \(4\) from both sides: \(5x=114 - 4\), \(5x = 110\).
Divide both sides by \(5\): \(x=\frac{110}{5}=22\).

Step2: Find the value of \(y\)

First, find the measure of \((3x - 24)^{\circ}\). Substitute \(x = 22\) into \(3x-24\), we get \(3\times22-24=66 - 24=42^{\circ}\).
The sum of angles around a point is \(360^{\circ}\), but here we can use the fact that the sum of adjacent angles forming a certain relationship. The sum of \(114^{\circ}\), \((3x - 24)^{\circ}\) and \((2y)^{\circ}\) (assuming a linear - pair or angle - sum property in the figure).
\(114+(3x - 24)+2y = 180\) (assuming a straight - line angle sum of \(180^{\circ}\)). Substitute \(x = 22\) into the equation:
\(114+(3\times22 - 24)+2y=180\).
\(114+(66 - 24)+2y=180\).
\(114 + 42+2y=180\).
\(156+2y=180\).
Subtract \(156\) from both sides: \(2y=180 - 156\), \(2y = 24\).
Divide both sides by \(2\): \(y = 12\).

Answer:

\(x = 22\), \(y = 12\)