∠1 and angle, 2∠2 are supplementary angles. If m, angle, 1, equals, left parenthesis, 5, x, plus, 30, right parenthesis, degreesm∠1=(5x+30) 
∘
  and m, angle, 2, equals, left parenthesis, x, plus, 30, right parenthesis, degreesm∠2=(x+30) 
∘
 , then find the measure of angle, 2∠2.

Since ∠1 and ∠2 are supplementary angles, their measures add up to 180°. This gives us the equation:

\[
m∠1 + m∠2 = 180°
\]

We are given:
- \( m∠1 = 5x + 30 \)
- \( m∠2 = x + 30 \)

Substituting these into the supplementary angle equation:

\[
(5x + 30) + (x + 30) = 180
\]

Now, simplify and solve for \(x\):

\[
6x + 60 = 180
\]

Subtract 60 from both sides:

\[
6x = 120
\]

Divide by 6:

\[
x = 20
\]

Now that we have \(x = 20\), substitute this value back into the expression for \(m∠2\):

\[
m∠2 = x + 30 = 20 + 30 = 50°
\]

Thus, the measure of \(∠2\) is 50°.

Would you like further details or have any questions? Here are some related questions to consider:

1. What is the measure of ∠1 with \(x = 20\)?
2. How do you know two angles are supplementary?
3. What would the angle sum be if the angles were complementary instead of supplementary?
4. If you increase the value of \(x\), how does it affect the measure of the angles?
5. How can you verify that two angles are supplementary?

**Tip:** Always double-check your calculations when solving for variables in geometry problems to avoid small mistakes.

∠1 and ∠2 are supplementary angles. If m∠1 = (5x + 30)° and m∠2 = (x + 30)°, then find the measure of ∠2.

Learn how to solve a problem involving supplementary angles, where m∠1 = (5x + 30)° and m∠2 = (x + 30)°. Find the measure of ∠2 using algebraic methods, suitable for students in Grades 7-9.

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