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The image shows a pentagon with five interior angles, each expressed as algebraic expressions. The goal here is to solve for \( x \) and find the value of each angle. The expressions for the angles are:

- \( (4x + 15)^\circ \)
- \( (4x + 15)^\circ \)
- \( (4x - 10)^\circ \)
- \( (4x - 10)^\circ \)
- \( (5x + 5)^\circ \)

### Step-by-step approach:
1. The sum of the interior angles of a pentagon is given by the formula:
\[
\text{Sum of interior angles} = 180(n - 2)
\]
where \( n \) is the number of sides. For a pentagon (\( n = 5 \)):
\[
\text{Sum of angles} = 180(5 - 2) = 180 \times 3 = 540^\circ
\]

2. Now, we can set up an equation where the sum of the given angles equals 540°:
\[
(4x + 15) + (4x + 15) + (4x - 10) + (4x - 10) + (5x + 5) = 540
\]

3. Simplifying the equation:
\[
(4x + 4x + 4x + 4x + 5x) + (15 + 15 - 10 - 10 + 5) = 540
\]
\[
21x + 15 = 540
\]

4. Solve for \( x \):
\[
21x = 540 - 15
\]
\[
21x = 525
\]
\[
x = \frac{525}{21} = 25
\]

### Final Step: Substituting \( x = 25 \) back into the angle expressions:
- \( (4x + 15)^\circ

Find the value of x and the interior angles of a pentagon with angle expressions (4x + 15)°, (4x + 15)°, (4x - 10)°, (4x - 10)°, and (5x + 5)°.

Learn how to solve for x and calculate the interior angles of a pentagon with given algebraic expressions. The sum of the angles is used to create and solve a linear equation. Suitable for students in Grades 8-10.

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