An angle measures 48° more than the measure of its complementary angle. What is the measure of each angle?

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.

Learn how to solve a problem involving complementary angles where one angle is 48° more than the other. This step-by-step guide covers key algebraic techniques and the complementary angles theorem. Suitable for students in Grades 6-8.

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