Two angles are complementary and the measure of one angle is 32 less than the other. What is the measure of the smaller angle?

Let's define the two complementary angles.

- Let one angle be \( x \).
- The other angle, being 32 degrees less, will be \( x - 32 \).

Since the angles are complementary, their sum is 90 degrees. Thus, we can set up the following equation:

\[
x + (x - 32) = 90
\]

Simplifying the equation:

\[
2x - 32 = 90
\]

Add 32 to both sides:

\[
2x = 122
\]

Now, divide both sides by 2:

\[
x = 61
\]

So, the larger angle is 61 degrees. The smaller angle is:

\[
x - 32 = 61 - 32 = 29
\]

Therefore, the measure of the smaller angle is **29 degrees**.

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. If two angles are supplementary and one is 20 less than the other, what are the angles?
2. What is the measure of each angle if two complementary angles are equal?
3. Find two angles if they are complementary and one is twice the other.
4. Two angles are complementary. If the larger angle is 70 degrees, what is the measure of the smaller angle?
5. If the difference between two complementary angles is 18 degrees, what are the measures of the two angles?

**Tip**: Always remember that complementary angles add up to 90°, while supplementary angles add up to 180°.

Learn how to find the measure of the smaller angle when two angles are complementary, and one is 32 degrees less than the other. This step-by-step solution uses algebraic techniques and is suitable for students in Grades 6-8.

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