The difference between the measures of two supplementary angles is 74degrees. Determine the measures of the two angles.
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Part 1
The larger angle has a measure of 
  
enter your response heredegrees.
The smaller angle has a measure of 
  
enter your response heredegrees.

Two angles are **supplementary** if their sum equals 180°. Let the two angles be represented as follows:

- Let \( x \) be the measure of the smaller angle.
- Then, \( x + 74 \) will be the measure of the larger angle, as their difference is given to be 74°.

Since the angles are supplementary, we know that:

\[
x + (x + 74) = 180
\]

Now, solve for \( x \):

\[
2x + 74 = 180
\]
\[
2x = 180 - 74
\]
\[
2x = 106
\]
\[
x = \frac{106}{2} = 53
\]

Thus, the smaller angle is \( 53^\circ \).

To find the larger angle:

\[
\text{Larger angle} = 53 + 74 = 127^\circ
\]

### Final Answer:
- The larger angle measures **127°**.
- The smaller angle measures **53°**.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. What are complementary angles, and how are they different from supplementary angles?
2. Can two acute angles be supplementary? Why or why not?
3. How would the problem change if the difference between the angles were 90°?
4. What is the general equation for two angles being supplementary with a given difference?
5. If the larger angle were obtuse, how could you verify your solution?

**Tip**: In problems involving supplementary angles, remember their sum will always equal 180°, which can simplify the setup of the equation.

The difference between the measures of two supplementary angles is 74 degrees. Determine the measures of the two angles.

Find the measures of two supplementary angles whose difference is 74°. This problem covers algebraic methods to solve for unknown angles, including the supplementary angles theorem. Suitable for students in Grades 6-8.

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