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The image contains a problem about "Finding Unknown Angle Measures in Linear Pairs" with the following details:

- There are two angles: ∠DEA and ∠AEB.
- The measure of ∠DEA is given as \( (x + 25)^\circ \).
- The measure of ∠AEB is given as \( (9x + 10)^\circ \).

Since ∠DEA and ∠AEB form a linear pair, their sum must be \( 180^\circ \) (because angles on a straight line add up to 180 degrees). 

Let's set up the equation:

\[
(x + 25) + (9x + 10) = 180
\]

Now, solving for \( x \):

\[
x + 25 + 9x + 10 = 180
\]
\[
10x + 35 = 180
\]
\[
10x = 180 - 35
\]
\[
10x = 145
\]
\[
x = 14.5
\]

Now, we can substitute \( x = 14.5 \) back into the expressions for the angle measures:

1. \( m\angle DEA = x + 25 = 14.5 + 25 = 39.5^\circ \)
2. \( m\angle AEB = 9x + 10 = 9(14.5) + 10 = 130.5 + 10 = 140.5^\circ \)

Thus:
- \( m\angle DEA = 39.5^\circ \)
- \( m\angle AEB = 140.5^\circ \)

Would you like more details on any step or have questions?

Here are five related questions to explore:

1. What are supplementary angles?
2. How do vertical angles relate to linear pairs?
3. If one angle of a linear pair is twice the other, how would you set up the equation?
4. How are adjacent angles different from linear pairs?
5. Can three or more angles on a straight line add up to more than 180°?

**Tip:** When solving for unknowns in linear pair problems, always remember the key property: their sum is always 180°.

What is the numerical sum of the degree measures of ∠DEA and ∠AEB?

Learn how to find unknown angle measures in linear pairs with the example of ∠DEA and ∠AEB. This problem involves solving an equation using algebra and the linear pair theorem, which states that angles on a straight line sum to 180°. Suitable for students in Grades 8-10.

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