https://file.aiquickdraw.com/mathbot/file/17262220047244iridldx.jpg

To solve this problem, let's define the angle and its supplement.

1. **Definition of Supplementary Angles**: Two angles are supplementary if their measures add up to \(180^\circ\).

2. **Set Up the Equations**: 
   - Let \(x\) be the measure of the angle.
   - Its supplement would be \(180 - x\).

3. **Translate the Problem into an Equation**:  
   The problem states: "The measure of an angle is 30 more than half the measure of its supplement."

   This translates to the equation:
   \[
   x = \frac{1}{2} (180 - x) + 30
   \]

4. **Solve for \(x\)**:

Let's solve the equation step-by-step:

\[
x = \frac{1}{2} (180 - x) + 30
\]

Multiply everything by 2 to eliminate the fraction:

\[
2x = 180 - x + 60
\]

Combine like terms:

\[
2x + x = 240 \implies 3x = 240
\]

\[
x = 80
\]

So, the measure of the angle is **80 degrees**.

5. **Verify the Solution**:  
   The supplement of 80 degrees is \(180 - 80 = 100\) degrees.  
   Half of 100 is 50, and 30 more than 50 is 80, which matches our solution.

Thus, the angle measures **80 degrees**.

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Would you like more details or have any questions?

### Related Questions:
1. What is the measure of the supplement of an angle that measures 45 degrees?
2. How would the equation change if the angle was 40 more than half its supplement?
3. Can two acute angles be supplementary?
4. What is the measure of an angle that is 20 less than half its supplement?
5. How do you determine if two angles are complementary?

### Tip:
When dealing with word problems, translating the problem statement into equations step-by-step can help make the solution process much easier!

The measure of an angle is 30 more than half the measure of its supplement.

Learn how to solve the problem where the measure of an angle is 30 more than half the measure of its supplement. This problem covers key geometric concepts, including supplementary angles and algebraic equations. Suitable for students in Grades 8-10.

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