Question

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

Explanation:

Step1: Identify the relationship for \( x \)

Since \( m \parallel n \), the alternate interior angles are equal. So, \( 7x + 15 = 6x + 19 \).

Step2: Solve for \( x \)

Subtract \( 6x \) from both sides: \( 7x - 6x + 15 = 6x - 6x + 19 \), which simplifies to \( x + 15 = 19 \). Then subtract 15 from both sides: \( x + 15 - 15 = 19 - 15 \), so \( x = 4 \).

Step3: Find the measure of the angle

Substitute \( x = 4 \) into \( 6x + 19 \): \( 6(4) + 19 = 24 + 19 = 43^\circ \).

Step4: Find \( y \)

The angle \( y \) and the angle \( 6x + 19 \) are supplementary (they form a linear pair), so \( y + (6x + 19) = 180 \). We know \( 6x + 19 = 43 \), so \( y + 43 = 180 \). Subtract 43 from both sides: \( y = 180 - 43 = 137 \).

Answer:

\( x = 4 \), \( y = 137 \)