The measure of the supplement of an angle exceeds 4 times the measure of the complement by 9. Find the measure of the complement.

Let's break down the problem step by step:

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

2. The supplement of an angle is given by \( 180^\circ - x \), and the complement of the angle is \( 90^\circ - x \).

3. According to the problem, the measure of the supplement exceeds 4 times the measure of the complement by 9. So, we set up the equation:

\[
180^\circ - x = 4(90^\circ - x) + 9
\]

4. Now, let's solve this equation:

\[
180 - x = 4(90 - x) + 9
\]
\[
180 - x = 360 - 4x + 9
\]
\[
180 - x = 369 - 4x
\]

5. Move the terms involving \( x \) to one side and the constants to the other side:

\[
- x + 4x = 369 - 180
\]
\[
3x = 189
\]

6. Solve for \( x \):

\[
x = \frac{189}{3} = 63
\]

7. The angle \( x \) is \( 63^\circ \). Now, the complement of the angle is:

\[
90^\circ - x = 90^\circ - 63^\circ = 27^\circ
\]

Thus, the measure of the complement is \( 27^\circ \).

Would you like further details on the solution? 

Here are some related questions:
1. What is the relationship between supplementary and complementary angles?
2. Can you provide another example of a problem involving supplementary and complementary angles?
3. What happens if an angle exceeds its complement by a certain value?
4. How can you solve an equation involving multiple angles using algebra?
5. What real-world scenarios might involve supplementary and complementary angles?

**Tip:** Always remember, supplementary angles add up to \( 180^\circ \), and complementary angles add up to \( 90^\circ \).

Learn how to solve a problem involving supplementary and complementary angles, where the supplement exceeds 4 times the complement by 9. This step-by-step solution explores key algebraic concepts and angle relationships, suitable for students in Grades 7-9.

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