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.