https://file.aiquickdraw.com/mathbot/file/17254073741962sti2xrn.jpg

The problem presented in the image asks to determine the measures of two complementary angles, \( \angle 1 \) and \( \angle 2 \).

### Given:
- The angles \( \angle 1 \) and \( \angle 2 \) are complementary, meaning their sum is 90°.
- \( m\angle 1 = (2x + 15)^\circ \)
- \( m\angle 2 = (4x - 3)^\circ \)

### To Find:
- The values of \( \angle 1 \) and \( \angle 2 \).

### Solution:
Since the angles are complementary, their sum is:
\[
m\angle 1 + m\angle 2 = 90^\circ
\]

Substituting the given expressions:
\[
(2x + 15) + (4x - 3) = 90
\]

Combine like terms:
\[
6x + 12 = 90
\]

Subtract 12 from both sides:
\[
6x = 78
\]

Divide by 6:
\[
x = 13
\]

### Now, substitute \( x = 13 \) back into the expressions for \( m\angle 1 \) and \( m\angle 2 \):
\[
m\angle 1 = 2(13) + 15 = 26 + 15 = 41^\circ
\]
\[
m\angle 2 = 4(13) - 3 = 52 - 3 = 49^\circ
\]

### Final Answer:
- \( m\angle 1 = 41^\circ \)
- \( m\angle 2 = 49^\circ \)

These measures confirm that \( 41^\circ + 49^\circ = 90^\circ \), so the solution is consistent.

Would you like further details or have any questions?

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Here are 5 related questions:
1. What would happen if \( \angle 1 \) and \( \angle 2 \) were supplementary instead of complementary?
2. How would the equation change if one of the angles was expressed as \( 5x + 20 \) instead?
3. What are vertical angles, and how do they differ from complementary angles?
4. How would you solve for \( x \) if one angle was given in radians?
5. What is the relationship between the angles in a right triangle?

**Tip:** Remember that complementary angles always add up to 90°, and this concept is often useful in geometric proofs and problem-solving.

The angles shown are complementary angles. Determine the measures of ∠1 and ∠2.

This problem involves finding the measures of two complementary angles using algebraic expressions. Learn how to solve for ∠1 and ∠2, where their sum equals 90°. Suitable for students in Grades 6-8.

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