Question

1. (3x - 16)° (6x + 7)° (11y - 32)° l m 14. note: j || k and l || m

Explanation:

Step1: Identify supplementary angles

Since \( l \parallel m \), the angles \( (3x - 16)^\circ \) and \( (6x + 7)^\circ \) are supplementary (same - side interior angles). So, their sum is \( 180^\circ \).
\[
(3x - 16)+(6x + 7)=180
\]

Step2: Solve for \( x \)

Combine like terms:
\[
3x+6x-16 + 7=180\\
9x-9 = 180
\]
Add 9 to both sides:
\[
9x=180 + 9\\
9x=189
\]
Divide both sides by 9:
\[
x=\frac{189}{9}=21
\]

Step3: Find the measure of \( (6x + 7)^\circ \)

Substitute \( x = 21 \) into \( 6x+7 \):
\[
6\times21+7=126 + 7=133
\]

Step4: Identify vertical or corresponding angles

Since \( l\parallel m \), the angle \( (6x + 7)^\circ \) and \( (11y-32)^\circ \) are equal (vertical angles or corresponding angles). So,
\[
11y-32=133
\]

Step5: Solve for \( y \)

Add 32 to both sides:
\[
11y=133 + 32\\
11y=165
\]
Divide both sides by 11:
\[
y=\frac{165}{11}=15
\]

Answer:

\( x = 21 \), \( y=15 \)