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Let's break down the problem step by step and write an equation:

The problem says:

"Three times the measure of an angle is 15 less than the measure of its complement."

1. Let the measure of the angle be \( x \).

2. The complement of an angle is found by subtracting the angle from 90° because complementary angles add up to 90°. So, the measure of its complement will be \( 90 - x \).

3. The equation based on the problem is:
   \[
   3x = (90 - x) - 15
   \]
   This says that "three times the angle \( x \)" equals "the complement \( 90 - x \)" minus 15.

### Solving the equation:

\[
3x = 90 - x - 15
\]
\[
3x = 75 - x
\]
Now, add \( x \) to both sides to move all the \( x \)'s to one side:
\[
3x + x = 75
\]
\[
4x = 75
\]
Now, divide both sides by 4:
\[
x = \frac{75}{4} = 18.75
\]

So, the measure of the angle is **18.75°**.

To find the complement, subtract this from 90:
\[
90 - 18.75 = 71.25°
\]

Thus, the angle is 18.75°, and its complement is 71.25°.

Would you like further details or have any questions about the solution? Here are a few related problems to consider:

1. What is the complement of an angle of 30°?
2. How do you solve for angles that are supplementary (adding up to 180°)?
3. Can two angles be complementary if one is obtuse?
4. If an angle is half of its complement, how do you set up the equation to solve it?
5. What are the properties of complementary and supplementary angles?

**Tip**: Always double-check that your equation correctly represents the relationship described in the problem before solving.

Three times the measure of an angle is 15 less than the measure of its complement.

Learn how to find the measure of an angle when three times the angle is 15 less than its complement. This problem involves algebraic manipulation and understanding complementary angles. Suitable for students in Grades 8-10.

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