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The problem asks to find the measures of an angle and its complement, where one angle is 24 degrees more than the other.

We can solve this problem using algebra.

Let the smaller angle be \( x \) degrees. Since the angles are complementary, their sum is 90 degrees, and the larger angle would be \( x + 24 \) degrees.

### Step 1: Set up the equation
\[
x + (x + 24) = 90
\]

### Step 2: Simplify and solve for \( x \)
\[
2x + 24 = 90
\]
\[
2x = 90 - 24
\]
\[
2x = 66
\]
\[
x = 33
\]

So, the smaller angle is 33 degrees.

### Step 3: Find the measure of the larger angle
\[
x + 24 = 33 + 24 = 57
\]

### Final Answer:
- The smaller angle is **33 degrees**.
- The larger angle is **57 degrees**.

Would you like more details or have any questions?

Here are five related questions to explore:
1. What are supplementary angles and how do they differ from complementary angles?
2. Can two angles both be greater than 45 degrees and still be complementary?
3. How would the solution change if the larger angle were 30 degrees more than the smaller angle?
4. If one angle is twice the other, what would the measures of the two complementary angles be?
5. How can complementary angles be used in real-world applications like construction or design?

**Tip:** Remember, complementary angles always add up to 90 degrees!

Find the measures of an angle and its complement if one angle measures 24 degrees more than the other.

Solve for the measures of two complementary angles, where one angle is 24 degrees more than the other. This problem involves algebraic expressions and is suitable for students in Grades 6-8.

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