Two angles are supplementary. The larger angle is 15 degrees more than the smaller angle. Find the measure Of both angles

Let the measure of the smaller angle be \( x \) degrees. Since the two angles are supplementary, their sum must be \( 180^\circ \).

According to the problem, the larger angle is 15 degrees more than the smaller angle. Therefore, the measure of the larger angle is \( x + 15 \) degrees.

### Set up the equation
Since the two angles add up to 180 degrees, we can write:
\[
x + (x + 15) = 180
\]

### Solve for \( x \)
1. Combine like terms:
   \[
   2x + 15 = 180
   \]
2. Subtract 15 from both sides:
   \[
   2x = 165
   \]
3. Divide by 2:
   \[
   x = 82.5
   \]

So, the smaller angle is \( 82.5^\circ \).

### Find the larger angle
The larger angle is \( x + 15 \):
\[
82.5 + 15 = 97.5
\]

### Conclusion
The measures of the two angles are:
- **Smaller angle**: \( 82.5^\circ \)
- **Larger angle**: \( 97.5^\circ \)

Would you like a more detailed explanation, or do you have any questions?

---

1. What are supplementary and complementary angles?
2. How can we verify the solution in this problem?
3. What happens if the larger angle is a different amount more than the smaller angle?
4. How would this problem change if they were complementary instead?
5. Can we apply a similar approach if we only know the difference between two angles?

**Tip:** Always check if your solution meets the original problem’s conditions to ensure accuracy.

Two angles are supplementary. The larger angle is 15 degrees more than the smaller angle. Find the measure of both angles.

Learn how to find the measure of two supplementary angles where the larger angle is 15 degrees more than the smaller one. This problem involves key algebra and geometry concepts, suitable for students in Grades 6-8.

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