The image shows a problem where two angles are given in terms of algebraic expressions. The problem asks to find the measure of each marked angle, where the two expressions for the angles are:

• $(15x + 2)^\circ$
• $(10x + 3)^\circ$

These two angles seem to form a linear pair, which means they are supplementary (i.e., they add up to $180^\circ$).

Step-by-step solution:

Since the angles are supplementary, we can set up the equation:

$(15x + 2) + (10x + 3) = 180$

Now, simplify the equation:

$15x + 10x + 2 + 3 = 180$

$25x + 5 = 180$

Next, subtract 5 from both sides:

$25x = 175$

Now, divide both sides by 25:

$x = 7$

Finding the angles:

1. For the larger angle: $15x + 2$: $15(7) + 2 = 105 + 2 = 107^\circ$

2. For the smaller angle: $10x + 3$: $10(7) + 3 = 70 + 3 = 73^\circ$

Thus, the measures of the angles are:

• The larger angle measures $107^\circ$.
• The smaller angle measures $73^\circ$.

Would you like more details on this, or do you have any questions?

Here are 5 related questions for practice:

1. What are supplementary angles?
2. What are complementary angles, and how are they different from supplementary angles?
3. How do you find the value of a variable when given the sum of angles?
4. Can angles that are not on a straight line be supplementary?
5. How would the equation change if the angles were complementary instead of supplementary?

Tip: Always double-check whether the angles are complementary (add to 90°) or supplementary (add to 180°) when solving for unknown variables.