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We are given that angles \( \angle 1 \) and \( \angle 2 \) are supplementary angles. Supplementary angles add up to \( 180^\circ \). 

### Given information:
- \( m \angle 1 = (2x - 20)^\circ \)
- \( m \angle 2 = (3x + 15)^\circ \)
  
Since \( \angle 1 \) and \( \angle 2 \) are supplementary, we know:
\[
m \angle 1 + m \angle 2 = 180^\circ
\]

### Substituting the given expressions:
\[
(2x - 20) + (3x + 15) = 180
\]

### Combine like terms:
\[
2x + 3x - 20 + 15 = 180
\]
\[
5x - 5 = 180
\]

### Solve for \( x \):
\[
5x = 185
\]
\[
x = \frac{185}{5} = 37
\]

### Now, find \( m \angle 2 \):
\[
m \angle 2 = 3x + 15 = 3(37) + 15 = 111 + 15 = 126^\circ
\]

Thus, the measure of \( \angle 2 \) is **126°**.

Would you like further details or have any questions?

Here are 5 related questions to expand on this concept:
1. What is the measure of \( \angle 1 \) given that \( x = 37 \)?
2. How do we classify angles that sum up to 90° instead of 180°?
3. What are the properties of complementary and supplementary angles?
4. How would the solution change if the angles were not supplementary but complementary?
5. What other angle relationships can you derive using algebraic expressions?

**Tip:** Always substitute your solution for \( x \) back into the original equations to check your work!

∠1 and ∠2 are supplementary angles. If m∠1 = (2x - 20)° and m∠2 = (3x + 15)°, then find the measure of ∠2.

Learn how to solve for the measure of ∠2 when ∠1 and ∠2 are supplementary angles with given algebraic expressions for each. This problem demonstrates key algebraic techniques and the application of the supplementary angle theorem.

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