∠1 and angle, 2∠2 are supplementary angles. If m, angle, 1, equals, left parenthesis, x, plus, 2, right parenthesis, degreesm∠1=(x+2) 
∘
  and m, angle, 2, equals, left parenthesis, 3, x, minus, 26, right parenthesis, degreesm∠2=(3x−26) 
∘
 , then find the measure of angle, 1∠1.

We are given that ∠1 and ∠2 are supplementary angles. Supplementary angles add up to \( 180^\circ \). This gives us the equation:

\[
m\angle1 + m\angle2 = 180^\circ
\]

### Step 1: Express the angles in terms of \(x\).

We are told:
\[
m\angle1 = (x + 2)^\circ
\]
\[
m\angle2 = (3x - 26)^\circ
\]

### Step 2: Set up the equation for supplementary angles.

\[
(x + 2) + (3x - 26) = 180
\]

### Step 3: Solve for \(x\).

Combine like terms:
\[
x + 3x + 2 - 26 = 180
\]
\[
4x - 24 = 180
\]

Add 24 to both sides:
\[
4x = 204
\]

Now divide by 4:
\[
x = 51
\]

### Step 4: Find the measure of \( \angle1 \).

Substitute \(x = 51\) into the expression for \( m\angle1 \):

\[
m\angle1 = (x + 2) = 51 + 2 = 53^\circ
\]

Thus, the measure of \( \angle1 \) is \( 53^\circ \).

### Summary:
The measure of \( \angle1 \) is \( 53^\circ \).

Would you like further clarification on this solution?

Here are 5 related questions to explore:

1. What is the measure of \( \angle2 \) in this problem?
2. How would you solve for \( x \) if the angles were complementary instead of supplementary?
3. Can you have two supplementary angles where both are equal? Why or why not?
4. What would happen if the measure of one angle was negative? Is that possible?
5. How can we verify that the two angles are indeed supplementary after solving?

**Tip:** Remember, supplementary angles always add up to \(180^\circ\), while complementary angles add up to \(90^\circ\).

∠1 and ∠2 are supplementary angles. If m∠1 = (x + 2)° and m∠2 = (3x − 26)°, then find the measure of ∠1.

Find out how to solve for the measure of an angle when two angles are supplementary. This problem involves basic algebra and geometry, using the equation m∠1 = (x + 2)° and m∠2 = (3x − 26)°. Suitable for students in Grades 7-10.

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