Question

1. (13y - 17)° (29x - 3)° (15x + 7)° l m

Explanation:

Step1: Identify supplementary angles

The angles \((29x - 3)^\circ\) and \((15x + 7)^\circ\) are supplementary (they form a linear pair), so their sum is \(180^\circ\).
\[
(29x - 3)+(15x + 7)=180
\]

Step2: Solve for \(x\)

Combine like terms:
\[
44x + 4 = 180
\]
Subtract 4 from both sides:
\[
44x = 176
\]
Divide by 44:
\[
x = 4
\]

Step3: Find the measure of \((29x - 3)^\circ\)

Substitute \(x = 4\):
\[
29(4)-3 = 116 - 3 = 113^\circ
\]

Step4: Identify corresponding angles

The angle \((13y - 17)^\circ\) is equal to \((29x - 3)^\circ\) (corresponding angles, since lines \(l\) and \(m\) are parallel? Or alternate - if the lines are parallel, corresponding or alternate interior/exterior angles are equal. Assuming the lines are parallel, so \((13y - 17)^\circ=(29x - 3)^\circ = 113^\circ\)

Step5: Solve for \(y\)

Set up the equation:
\[
13y - 17 = 113
\]
Add 17 to both sides:
\[
13y = 130
\]
Divide by 13:
\[
y = 10
\]

Answer:

\(x = 4\), \(y = 10\) (If you need the measures of angles: \((29x - 3)^\circ=113^\circ\), \((15x + 7)^\circ = 67^\circ\), \((13y - 17)^\circ=113^\circ\))