https://file.aiquickdraw.com/mathbot/file/1725982318645ra9dfhyz.jpg

The image presents an angle relationship problem, where you need to solve for \(x\) and \(y\) using the given expressions for angles. Based on the diagram, there are two intersecting lines, labeled \(l\) and \(m\), with several angle expressions provided.

### Key Information:
- The angle on the left is given as \(8y + 17^\circ\).
- The angle adjacent to it (vertically opposite angle) is given as \(6x - 7^\circ\).
- Another angle below that one is given as \(3x - 29^\circ\).

From angle relationships, we know that vertically opposite angles are congruent (equal). Therefore, we can set up equations based on this fact:

### Step 1: Solve for \(x\)
Using vertically opposite angles, we can equate \(6x - 7\) to \(3x - 29\):
\[
6x - 7 = 3x - 29
\]
Solve for \(x\):
\[
6x - 3x = -29 + 7
\]
\[
3x = -22
\]
\[
x = \frac{-22}{3} \quad \text{or} \quad x = -\frac{22}{3}
\]

### Step 2: Plug \(x\) into the second equation to find \(y\)
We can use the fact that the sum of angles on a straight line is \(180^\circ\) (linear pair). So, the sum of the angles \(8y + 17^\circ\) and \(3x - 29^\circ\) should equal \(180^\circ\):
\[
(8y + 17) + (3x - 29) = 180
\]
Substitute \(x = -\frac{22}{3}\) into this equation to solve for \(y\).

Let me calculate the exact values of \(y\) for you.

Solve for x and y using the given angle relationships where the angle on the left is given as (8y + 17) degrees and adjacent angles (vertically opposite) are (6x - 7) degrees and (3x - 29) degrees.

Discover how to solve for x and y with angle relationships in intersecting lines, using theorems on vertically opposite angles and linear pairs. Suitable for students in Grades 7 to 10, this problem challenges understanding of geometry and algebra combined.

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