The problem shown in the image requires finding the measures of each marked angle in the diagram, with some given algebraic expressions for the angles.

The given information:

1. One of the angles in the triangle is $(2x - 10)^\circ$.
2. Another angle in the triangle is $(x - 6)^\circ$.
3. The exterior angle on the right side of the diagram is given as $(8x - 196)^\circ$.
4. The solution mentions that the top angle, $(2x - 10)^\circ$, is equal to $88^\circ$.

Step-by-step solution:

1. From the image, we know that: $2x - 10 = 88^\circ$ Solving for $x$: $2x = 88 + 10$ $2x = 98$ $x = 49$

2. Now, substitute $x = 49$ into the other two expressions to find the measures of the other angles.

   • The angle $(x - 6)^\circ$: $x - 6 = 49 - 6 = 43^\circ$

   • The exterior angle $(8x - 196)^\circ$: $8x - 196 = 8(49) - 196 = 392 - 196 = 196^\circ$

Conclusion:

• The top angle is $88^\circ$.
• The left angle is $43^\circ$.
• The exterior angle on the right side is $196^\circ$.

Would you like more details or have any further questions?

Here are 5 related questions to expand on this topic:

1. How can you verify that the angles of a triangle sum up to $180^\circ$ using this example?
2. What is the relationship between an exterior angle and the interior angles of a triangle?
3. How do you solve for unknown angles in more complex polygons?
4. How can we apply algebra to solve problems involving angles in circles?
5. Can you explain how alternate interior angles and corresponding angles work in parallel line situations?

Tip: When solving for unknown angles in a triangle, remember that the sum of the interior angles of any triangle always equals $180^\circ$.