https://file.aiquickdraw.com/mathbot/file/1727301709339to1xkf07.jpg

In the given image, the problem provides two angles of a triangle and asks to find the value of \( x \). Specifically:

- \( m\angle 1 = 20^\circ \)
- \( m\angle 2 = 60^\circ \)

Looking at the diagram, it appears to be a right triangle, where one angle is \( 90^\circ \). This allows us to calculate \( x \), as all angles in a triangle sum to \( 180^\circ \).

### Steps to Solve:
1. In any triangle, the sum of the interior angles is always \( 180^\circ \).
   
2. Given:
   - \( m\angle 1 = 20^\circ \)
   - \( m\angle 2 = 60^\circ \)
   - \( m\angle 3 = x \) (the third angle)
   
   The sum of the angles of the triangle will be:
   \[
   20^\circ + 60^\circ + x = 180^\circ
   \]
   
3. Solve for \( x \):
   \[
   x = 180^\circ - (20^\circ + 60^\circ) = 180^\circ - 80^\circ = 100^\circ
   \]

Thus, the value of \( x \) is \( 100^\circ \).

Would you like more details on this solution? Here are 5 related questions that might interest you:

1. What is the sum of the interior angles in any polygon, and how is it calculated for different shapes?
2. How do you solve problems involving right triangles using trigonometric ratios like sine, cosine, and tangent?
3. Can you explain the relationship between interior and exterior angles in polygons?
4. What is the significance of the right angle in trigonometry and geometry?
5. How do supplementary and complementary angles relate to solving geometric problems?

**Tip:** When solving triangle problems, always verify the type of triangle (right, isosceles, equilateral) to determine which properties or theorems apply.

Given m∠1 = 20° and m∠2 = 60°, find the value of x.

This geometry problem asks to find the third angle in a triangle when given m∠1 = 20° and m∠2 = 60°. Using the Triangle Angle Sum Theorem, you can calculate the missing angle. Ideal for students in Grades 7-9.

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