Question

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

Explanation:

Step1: Identify supplementary angles

The angles \((9x + 2)^\circ\) and \((3x - 14)^\circ\) are supplementary (they form a linear pair), so their sum is \(180^\circ\).
\[
(9x + 2) + (3x - 14) = 180
\]

Step2: Solve for \(x\)

Combine like terms:
\[
12x - 12 = 180
\]
Add 12 to both sides:
\[
12x = 192
\]
Divide by 12:
\[
x = 16
\]

Step3: Find \(y\)

First, find the measure of \((9x + 2)^\circ\) by substituting \(x = 16\):
\[
9(16) + 2 = 144 + 2 = 146^\circ
\]
Now, \((9x + 2)^\circ\) and \(y^\circ\) are supplementary (linear pair), so:
\[
y + 146 = 180
\]
Subtract 146 from both sides:
\[
y = 34
\]

Answer:

\(x = 16\), \(y = 34\)