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The problem presents a triangle where the sum of the angles is 180°. The angles in the triangle are given as 110°, \( 5x^\circ \), and \( 2x^\circ \). We can solve for \( x \) using the angle sum property of triangles.

### Step 1: Set up the equation
The sum of the angles in any triangle is always 180°. Therefore, we can write:
\[
110^\circ + 5x^\circ + 2x^\circ = 180^\circ
\]

### Step 2: Solve for \( x \)
Combine like terms:
\[
110^\circ + 7x^\circ = 180^\circ
\]
Now subtract 110° from both sides:
\[
7x^\circ = 70^\circ
\]
Finally, divide by 7:
\[
x = 10^\circ
\]

### Step 3: Find the values of \( 5x \) and \( 2x \)
- \( 5x = 5 \times 10^\circ = 50^\circ \)
- \( 2x = 2 \times 10^\circ = 20^\circ \)

### Final Answer:
- \( x = 10^\circ \)
- \( 5x = 50^\circ \)
- \( 2x = 20^\circ \)

Would you like further clarification on any of the steps?

### Related Questions:
1. What is the general formula for the sum of angles in any polygon?
2. How do you calculate the angles of a regular polygon?
3. Can you apply the same method to find angles in quadrilaterals?
4. What are alternate methods for finding missing angles in a triangle?
5. How do angle measures change when extending the sides of polygons?

### Tip:
Always remember that the sum of the interior angles of a triangle is 180°, which is a useful property for solving many geometric problems.

Find the value of x. Then find the missing angle measures of the polygon. The triangle has angles 5x°, 2x°, and 110°. The sum of angles is 180°.

Solve a geometry problem involving the angle sum property of triangles. Learn how to find the value of x when given angles 5x°, 2x°, and 110°, and how to calculate the missing angle measures. Suitable for Grades 6-8 students.

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