∠1 and angle, 2∠2 are supplementary angles. If m, angle, 1, equals, left parenthesis, x, plus, 26, right parenthesis, degreesm∠1=(x+26) 
∘
  and m, angle, 2, equals, left parenthesis, 2, x, plus, 22, right parenthesis, degreesm∠2=(2x+22) 
∘
 , then find the measure of angle, 2∠2.

Supplementary angles sum to \(180^\circ\). This means that:

\[
m\angle 1 + m\angle 2 = 180^\circ
\]

Given:
\[
m\angle 1 = (x + 26)^\circ \quad \text{and} \quad m\angle 2 = (2x + 22)^\circ
\]

Substitute the given values into the equation:

\[
(x + 26) + (2x + 22) = 180
\]

Simplify the equation:

\[
x + 26 + 2x + 22 = 180
\]
\[
3x + 48 = 180
\]

Now, solve for \(x\):

\[
3x = 180 - 48
\]
\[
3x = 132
\]
\[
x = \frac{132}{3} = 44
\]

Now that we have \(x = 44\), substitute this value back into the expression for \(m\angle 2\):

\[
m\angle 2 = 2x + 22 = 2(44) + 22 = 88 + 22 = 110^\circ
\]

Thus, the measure of \( \angle 2 \) is:

\[
m\angle 2 = 110^\circ
\]

### Do you need further details or explanations on any part?

Here are 5 related questions to extend your understanding:
1. What is the definition of complementary angles?
2. How would you solve if the angles were complementary instead of supplementary?
3. Can two obtuse angles be supplementary? Why or why not?
4. If the angles were both given in terms of a different variable, how would the solution process change?
5. What are some real-world applications of supplementary angles?

**Tip:** Always verify your solution by checking if the sum of the angles equals the expected total (in this case, \(180^\circ\)).

∠1 and ∠2 are supplementary angles. If m∠1 = (x + 26)° and m∠2 = (2x + 22)°, then find the measure of ∠2.

This problem demonstrates how to solve for supplementary angles using algebraic expressions. We are given m∠1 = (x + 26)° and m∠2 = (2x + 22)° and find that m∠2 equals 110°. Suitable for students in Grades 8-10, this step-by-step guide covers core algebra and geometry concepts.

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