https://file.aiquickdraw.com/mathbot/file/1726538854292350tltlt.jpg

To solve the problem in the image, we need to use the fact that the two angles given, ∠1 and ∠2, form a right angle, which sums up to 90°. 

### Step-by-step solution:
1. From the diagram and the problem description:
   \[
   m∠1 = 2x° \quad \text{and} \quad m∠2 = (x + 57)°
   \]
   
2. Since the two angles are complementary (they add up to 90° because they form a right angle), we can write the equation:
   \[
   2x + (x + 57) = 90
   \]

3. Simplify and solve for \( x \):
   \[
   2x + x + 57 = 90
   \]
   \[
   3x + 57 = 90
   \]
   Subtract 57 from both sides:
   \[
   3x = 33
   \]
   Divide by 3:
   \[
   x = 11
   \]

4. Now that we have \( x = 11 \), substitute back into the expressions for the angles:
   \[
   m∠1 = 2x = 2(11) = 22°
   \]
   \[
   m∠2 = x + 57 = 11 + 57 = 68°
   \]

Thus, the measures of the angles are:
- \( m∠1 = 22° \)
- \( m∠2 = 68° \)

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

### Related questions:
1. How do we know when two angles are complementary?
2. What would the equation look like if the two angles formed a straight line (180°)?
3. What happens if we had three angles summing up to 90°? How would the equation change?
4. If one angle was a constant value (e.g., 45°), how would that affect the problem?
5. What other geometrical relationships can help solve for angles in a triangle?

**Tip:** When angles form a right angle (90°), they are always complementary, meaning their measures will always add up to 90°.

In the figure below, m∠1 = 2x° and m∠2 = (x + 57)°. Find the angle measures.

Solve the geometry problem where m∠1 = 2x° and m∠2 = (x + 57)°. Learn how to set up the equation for complementary angles and solve for x to find the angle measures. Suitable for students in Grades 7-9.

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