∠1 and angle, 2∠2 are supplementary angles. If m, angle, 1, equals, left parenthesis, 3, x, minus, 28, right parenthesis, degreesm∠1=(3x−28)
∘
and m, angle, 2, equals, left parenthesis, x, minus, 4, right parenthesis, degreesm∠2=(x−4)
∘
, then find the measure of angle, 1∠1.

Given that ∠1 and ∠2 are supplementary angles, their measures add up to 180°.

### Step 1: Set up the equation
Since the sum of ∠1 and ∠2 is 180°, we can write the equation as:
\[
m∠1 + m∠2 = 180°
\]

Substitute the given expressions for \( m∠1 \) and \( m∠2 \):
\[
(3x - 28) + (x - 4) = 180
\]

### Step 2: Simplify the equation
Combine like terms:
\[
3x - 28 + x - 4 = 180
\]
\[
4x - 32 = 180
\]

### Step 3: Solve for \( x \)
Add 32 to both sides:
\[
4x = 212
\]

Now, divide both sides by 4:
\[
x = 53
\]

### Step 4: Find the measure of ∠1
Substitute \( x = 53 \) back into the expression for \( m∠1 \):
\[
m∠1 = 3x - 28 = 3(53) - 28 = 159 - 28 = 131°
\]

Thus, the measure of ∠1 is **131°**.

Would you like more details or have any questions? Here are some related problems:

1. What is the measure of ∠2 if \( x = 53 \)?
2. How do you determine if two angles are supplementary?
3. What are complementary angles, and how do they differ from supplementary angles?
4. Can two obtuse angles be supplementary? Why or why not?
5. What happens to the value of \( x \) if the measures of ∠1 and ∠2 were equal?

**Tip:** When solving problems with supplementary angles, remember that their measures always sum to 180°, which is a key property to set up your equations.

Discover how to find the measure of angle 1 in a problem involving supplementary angles. Step-by-step solution provided with equations and calculations. Suitable for Grades 9-12.

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