Question

answer attempt 1 out of 2

x =

y =

Explanation:

Step1: Find the value of \(x\)

Since \((2x + 7)^{\circ}\) and \((3x-15)^{\circ}\) are vertical angles, they are equal.
So, \(2x+7 = 3x - 15\)
\(2x-3x=-15 - 7\)
\(-x=-22\)
\(x = 22\)

Step2: Find the value of \(y\)

\((y + 16)^{\circ}\) and \((2x+7)^{\circ}\) are supplementary angles (they form a linear pair).
Substitute \(x = 22\) into \(2x+7\): \(2\times22+7=44 + 7=51^{\circ}\)
Since \((y + 16)+(2x + 7)=180\)
\(y+16+51 = 180\)
\(y+67=180\)
\(y=180 - 67\)
\(y = 113\)

Answer:

\(x = 22\), \(y = 113\)