The problem shown in the image states:

"Two angles are complementary. One angle is 6° less than the other angle. Find the measures of the angles."

Solution:

• Let the larger angle be $x$.
• The smaller angle will be $x - 6$ because it's 6 degrees less than the larger angle.

Since the two angles are complementary, their sum is 90°:

$x + (x - 6) = 90$

Now, solve for $x$:

$2x - 6 = 90$ $2x = 96$ $x = 48$

The larger angle is 48°, and the smaller angle is:

$x - 6 = 48 - 6 = 42$

Answer:

• The smaller angle is 42°.

Would you like further details or have any questions?

Here are 5 related questions:

1. What are supplementary angles?
2. How do you solve for an angle if it's given as a fraction of another angle?
3. What happens when two angles are congruent?
4. How do you find the third angle in a triangle when two are given?
5. Can complementary angles be obtuse?

Tip: Complementary angles always add up to 90°, so if you know one angle, you can easily find the other by subtracting from 90.