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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.

Find the measure of each marked angle. The two given angles are expressed as (15x + 2)° and (10x + 3)°.

Learn how to find the measure of two angles given as algebraic expressions (15x + 2)° and (10x + 3)° that form a linear pair. This problem involves setting up and solving a linear equation, suitable for students in Grades 8-10.

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