Question

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

Explanation:

Step1: Solve for \( x \)

Since \( m \parallel n \), the corresponding angles \( 3x + 17 \) and \( 6x - 16 \) are equal (corresponding angles postulate). So we set up the equation:
\( 3x + 17 = 6x - 16 \)
Subtract \( 3x \) from both sides:
\( 17 = 3x - 16 \)
Add 16 to both sides:
\( 33 = 3x \)
Divide both sides by 3:
\( x = 11 \)

Step2: Find the measure of the angle

First, substitute \( x = 11 \) into \( 3x + 17 \):
\( 3(11) + 17 = 33 + 17 = 50^\circ \)
Now, the angle \( (2y + 14)^\circ \) and \( (3x + 17)^\circ \) are supplementary (linear pair), so:
\( 2y + 14 + 50 = 180 \)
Simplify:
\( 2y + 64 = 180 \)
Subtract 64 from both sides:
\( 2y = 116 \)
Divide by 2:
\( y = 58 \)

Answer:

\( x = 11 \), \( y = 58 \)