∠A and ∠B∠B are a pair of supplementary angles, where ∠A∠A =30+2x30+2*x*  and∠B∠B=x

Given that ∠A and ∠B are supplementary angles, their sum must equal 180°. We can write the equation:

\[
\angle A + \angle B = 180°
\]

From the problem, we know:

\[
\angle A = 30 + 2x
\]
\[
\angle B = x
\]

Substituting these expressions into the equation for supplementary angles:

\[
(30 + 2x) + x = 180°
\]

Now, solve for \( x \):

\[
30 + 3x = 180
\]

Subtract 30 from both sides:

\[
3x = 150
\]

Now, divide by 3:

\[
x = 50
\]

Thus, \( x = 50 \).

### Now, calculate the individual angles:

\[
\angle A = 30 + 2x = 30 + 2(50) = 30 + 100 = 130°
\]
\[
\angle B = x = 50°
\]

So, \( \angle A = 130° \) and \( \angle B = 50° \).

Would you like further details on this? 

Here are 5 related questions to expand your understanding:
1. What are complementary angles, and how do they differ from supplementary angles?
2. How would the equation change if ∠A were \(2x + 30\) instead of \(30 + 2x\)?
3. If the angles were complementary, what would be the value of \(x\)?
4. Can you find another pair of supplementary angles where the expressions are different but still add up to 180°?
5. How would you solve this if one angle was given in terms of trigonometric functions?

**Tip:** Always check the conditions of angle pairs, like supplementary or complementary, as they define the sum of the angles (180° or 90° respectively).

∠A and ∠B are a pair of supplementary angles, where ∠A = 30 + 2x and ∠B = x. Solve for x and find the individual angles.

Learn how to solve for x in a pair of supplementary angles where ∠A = 30 + 2x and ∠B = x. Understand key concepts like algebra and supplementary angles and follow a step-by-step solution. Suitable for students in Grades 8-10.

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