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It looks like you're working on a geometry homework problem involving angles and algebraic expressions. From the image, the task is to solve for the measures of two angles represented in terms of \(x\). Here's what I can see:

- The angles are given as \( m \angle = 2x + 20^\circ \) and \( m \angle = 2x + 50^\circ \).
- There is a diagram suggesting that these angles are either supplementary or complementary.

To help you solve the problem, you need to first determine the relationship between the angles. If the angles are **supplementary**, their sum will be \(180^\circ\). If they are **complementary**, their sum will be \(90^\circ\).

**Assuming the angles are supplementary**:

\[
(2x + 20^\circ) + (2x + 50^\circ) = 180^\circ
\]

Simplifying:

\[
4x + 70^\circ = 180^\circ
\]

Now, subtract 70 from both sides:

\[
4x = 110^\circ
\]

Finally, divide by 4:

\[
x = 27.5^\circ
\]

You can now substitute this value back into the expressions for the angles to find their measures.

1. For \( m \angle = 2x + 20^\circ \):

\[
m \angle = 2(27.5) + 20 = 55 + 20 = 75^\circ
\]

2. For \( m \angle = 2x + 50^\circ \):

\[
m \angle = 2(27.5) + 50 = 55 + 50 = 105^\circ
\]

Thus, the two angles are \( 75^\circ \) and \( 105^\circ \), and they are supplementary since \( 75^\circ + 105^\circ = 180^\circ \).

Would you like more details or have any other questions?

Here are 5 related questions to deepen your understanding:

1. What are complementary angles and how do you identify them?
2. Can you solve for angles if the two given angles are complementary?
3. How does algebra help in solving geometric angle problems?
4. How would the solution change if the two angles were instead part of a triangle?
5. Can you solve a similar problem where the angles are expressed differently?

**Tip**: Always double-check the relationships between angles (e.g., supplementary, complementary) to avoid calculation errors!

Use an algebraic equation to find the measure of each angle represented in terms of x: m ∠ = 2x + 20° and m ∠ = 2x + 50°.

Learn how to solve for the measures of angles expressed algebraically. This problem involves using algebra to solve angle measures with supplementary angle relationships. Suitable for students in Grades 7-9.

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