The measure of the supplement of an angle is three times the measure of the angle. Find the measures of the angle and its supplement.

Let the measure of the angle be \( x \). The supplement of an angle is given by \( 180^\circ - x \). According to the problem, the supplement is three times the measure of the angle, so we can set up the following equation:

\[
180^\circ - x = 3x
\]

### Solving for \( x \):
1. Add \( x \) to both sides to combine like terms:
   \[
   180^\circ = 4x
   \]

2. Divide both sides by 4:
   \[
   x = \frac{180^\circ}{4} = 45^\circ
   \]

So, the measure of the angle is \( 45^\circ \).

### Finding the Supplement:
The supplement of the angle is:
\[
180^\circ - 45^\circ = 135^\circ
\]

Thus, the angle is \( 45^\circ \), and its supplement is \( 135^\circ \).

Would you like more details or have any questions?

Here are five related questions:
1. What is the definition of complementary angles?
2. If the measure of the supplement were four times the angle, how would the solution change?
3. How do you find the complement of an angle?
4. What is the relationship between angles on a straight line?
5. How are angles in a triangle related to each other?

**Tip:** Always check your result by substituting the found values back into the original equation!

Learn how to find the measure of an angle and its supplement when the supplement is three times the measure of the angle. This detailed step-by-step solution involves algebraic techniques and understanding supplementary angles. Suitable for students in Grades 6-8.

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