https://file.aiquickdraw.com/mathbot/file/173016047953490g68tbx.jpg

To solve this problem, let’s break it down step-by-step:

### Problem Details:
1. Two angles are supplementary, which means their measures add up to 180°.
2. The larger angle is 102° more than the smaller angle.

### Steps to Solve:
1. Let the measure of the smaller angle be \( x \) (in degrees).
2. Then, the measure of the larger angle would be \( x + 102 \) (in degrees) based on the given information.
3. Since the angles are supplementary, their sum is 180°:
   \[
   x + (x + 102) = 180
   \]
4. Simplify and solve for \( x \):
   \[
   2x + 102 = 180
   \]
   \[
   2x = 180 - 102
   \]
   \[
   2x = 78
   \]
   \[
   x = 39
   \]
5. So, the smaller angle is 39°, and the larger angle is:
   \[
   39 + 102 = 141
   \]

### Final Answer:
- **The smaller angle is 39°**.
- **The larger angle is 141°**.

Would you like more details on this solution, or do you have any further questions?

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Here are five related questions to deepen understanding:
1. What are complementary angles, and how do they differ from supplementary angles?
2. How do you find the measures of angles if one angle is a given fraction of the other?
3. How can this method be applied to find angles in a triangle if one angle is known?
4. How would this solution change if the two angles were not supplementary but formed a straight line with an additional third angle?
5. What real-life examples might involve supplementary angles?

**Tip:** Remember, when angles are supplementary, their sum will always be exactly 180 degrees.

Two angles are supplementary. The larger angle is 102° more than the smaller. Find the measures of both angles.

Learn how to solve for two supplementary angles where the larger angle is 102° more than the smaller. This solution involves algebraic equations and the supplementary angles theorem, ideal for students in Grades 6-8.

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