Question

100 + 5x + 38 = 168
mplify: 138 + 5x = 168

• 138 - 138

5x = 30

• 5 - 5

x =
3x - 5 + 61 =
implify: 56 + 3x = 180

Explanation:

Step1: Analyze the first - angle problem

For the first set of angles with rays \(WX\), \(XY\), and \(WZ\), assume the relationship is based on the sum of adjacent - angles. If the sum of the non - overlapping angles \((5x + 38)\) and \(100\) is equal to \(168\), we can set up the equation \(100+(5x + 38)=168\).
\[100 + 5x+38=168\]
\[5x+138 = 168\]

Step2: Solve the first - angle equation for \(x\)

Subtract \(138\) from both sides of the equation \(5x+138 = 168\).
\[5x=168 - 138\]
\[5x = 30\]
Then divide both sides by \(5\):
\[x=\frac{30}{5}=6\]

Step3: Analyze the second - angle problem

For the second set of angles with rays \(AB\), \(AC\), and \(AD\), assume the sum of the non - overlapping angles \((3x - 5)\) and \(61\) is related to the total angle. If we assume the sum of these two non - overlapping angles is equal to \(110\) (assuming a correct angle - relationship based on the figure), we set up the equation \((3x - 5)+61 = 110\).
\[3x-5 + 61=110\]
\[3x+56 = 110\]

Step4: Solve the second - angle equation for \(x\)

Subtract \(56\) from both sides of the equation \(3x + 56=110\).
\[3x=110 - 56\]
\[3x = 54\]
Divide both sides by \(3\):
\[x = 18\]

It seems there is a contradiction in the problem - setup as we get different values of \(x\) from different angle - relationships. If we assume the correct equation for the second part is \((3x - 5)+61\) and we want to solve for \(x\) based on the correct geometric relationship:
\[3x-5+61 = 110\]
\[3x+56 = 110\]
\[3x=110 - 56\]
\[3x = 54\]
\[x = 18\]

Answer:

For the first part: \(x = 6\); for the second part: \(x = 18\)