Question

given ( m parallel n ), find the value of ( x ).
answer attempt 1 out of 2
( x = )

Explanation:

Step1: Identify supplementary angles

Since \( m \parallel n \) and \( t \) is a transversal, the angles \( (7x + 22)^\circ \) and \( (8x + 8)^\circ \) are supplementary (they form a linear pair). So, their sum is \( 180^\circ \).
\[
(7x + 22) + (8x + 8) = 180
\]

Step2: Combine like terms

Combine the \( x \)-terms and the constant terms:
\[
15x + 30 = 180
\]

Step3: Solve for \( x \)

Subtract 30 from both sides:
\[
15x = 180 - 30 \\
15x = 150
\]
Divide both sides by 15:
\[
x = \frac{150}{15} \\
x = 10
\]

Answer:

\( x = 10 \)