To solve the problem where the measure of an angle is nine times greater than its supplement, let's proceed step by step.

1. Define the variables:

   • Let $x$ represent the measure of the supplement of the angle.
   • The measure of the angle itself is given as $9x$.

2. Set up the equation:

   • The sum of an angle and its supplement is always 180 degrees.
   • Therefore, the equation can be written as: $x + 9x = 180$

3. Simplify the equation:

   • Combine like terms: $10x = 180$

4. Solve for $x$:

   • Divide both sides of the equation by 10: $x = \frac{180}{10} = 18$

So, the supplement of the angle is 18 degrees.

5. Find the measure of the angle:
   • Since the angle is nine times its supplement: $9x = 9 \times 18 = 162$

Thus, the angle measures 162 degrees, and its supplement is 18 degrees.

Would you like more details, or do you have any questions?

Here are 5 related questions:

1. What is the definition of supplementary angles?
2. How do you find the supplement of a given angle?
3. What would the equation look like if the angle was five times its supplement?
4. How can you verify that the angle and its supplement add up to 180 degrees?
5. What are complementary angles, and how do they differ from supplementary angles?

Tip: Always remember that the sum of supplementary angles is 180 degrees, regardless of the measures involved.