Two angles are supplementary. the measure of one angle is 58 more than the other. What is the measure of the smaller angle?

Let the two angles be represented as:

- One angle = \( x \)
- The other angle = \( x + 58 \) (since it is 58 degrees more than the other angle)

Since the angles are supplementary, their sum is 180°:

\[
x + (x + 58) = 180
\]

Now, solve for \( x \):

\[
2x + 58 = 180
\]
\[
2x = 180 - 58
\]
\[
2x = 122
\]
\[
x = \frac{122}{2} = 61
\]

So, the smaller angle is \( 61^\circ \).

Would you like further details or have any other questions?

Here are 5 related questions:
1. What is the measure of the larger angle in this case?
2. What if the difference between the angles was 45 instead of 58?
3. How do you define complementary angles, and how would you solve a similar problem with complementary angles?
4. What are the properties of supplementary angles in terms of their relationship to a straight line?
5. How can you calculate angles if given the ratio of their measures?

**Tip:** Supplementary angles always sum to 180°, while complementary angles sum to 90°.

Two angles are supplementary. The measure of one angle is 58 more than the other. What is the measure of the smaller angle?

Learn how to find the measure of the smaller angle when two supplementary angles have a difference of 58°. This step-by-step solution involves setting up and solving a linear equation. Suitable for students in Grades 6-8.

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