Let's solve this problem step by step.

Two angles are complementary if their measures add up to 90°.

Let the measure of the smaller angle be $x$. Since the problem states that the other angle is 48° more than the smaller angle, the measure of the larger angle will be $x + 48$.

Now, using the fact that complementary angles add up to 90°, we can set up the following equation:

$x + (x + 48) = 90$

Step 1: Combine like terms

$2x + 48 = 90$

Step 2: Subtract 48 from both sides

$2x = 90 - 48$ $2x = 42$

Step 3: Divide both sides by 2

$x = \frac{42}{2} = 21$

So, the smaller angle measures 21°.

Step 4: Find the larger angle

Since the larger angle is 48° more than the smaller angle: $x + 48 = 21 + 48 = 69$

Thus, the larger angle measures 69°.

Final Answer:

• The smaller angle is 21°.
• The larger angle is 69°.

Would you like further details or explanations?

Here are some related questions to explore:

1. What is the relationship between complementary and supplementary angles?
2. How do you solve a problem with angles that are supplementary?
3. Can two angles be both complementary and congruent?
4. What if the angle was 48° less than its complementary angle instead?
5. How do complementary angles apply in geometry, like in triangle problems?

Tip: Always double-check that complementary angles add up to 90° when solving these types of problems.