This problem is about complementary angles. Two angles are complementary if their sum is $90^\circ$. Let's solve the problem step by step.

Problem:

The measure of one angle is $24^\circ$ greater than its complement. We need to find the measures of the two angles.

Step 1: Let the angles be

• Let the smaller angle be $x$.
• Then, the larger angle is $x + 24^\circ$.

Step 2: Use the property of complementary angles

The sum of complementary angles is $90^\circ$, so: $x + (x + 24^\circ) = 90^\circ$

Step 3: Solve for $x$

$2x + 24^\circ = 90^\circ$ Subtract $24^\circ$ from both sides: $2x = 66^\circ$ Now, divide by 2: $x = 33^\circ$

Step 4: Find the measure of the other angle

The other angle is: $x + 24^\circ = 33^\circ + 24^\circ = 57^\circ$

Thus, the two angles are $33^\circ$ and $57^\circ$.

Answer:

The correct choice is C) 33° and 57°.

Would you like further details or explanations on any part of the solution?

Related Questions:

1. What is the definition of complementary angles?
2. How would this problem change if the angles were supplementary instead of complementary?
3. What is the sum of two supplementary angles?
4. How can we find the complement of an angle without setting up an equation?
5. If one angle is twice the size of its complement, what are the angles?

Tip: Always remember that complementary angles add up to $90^\circ$ and supplementary angles add up to $180^\circ$.