Math Problem Statement

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

Solution

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

  • m1=20m\angle 1 = 20^\circ
  • m2=60m\angle 2 = 60^\circ

Looking at the diagram, it appears to be a right triangle, where one angle is 9090^\circ. This allows us to calculate xx, as all angles in a triangle sum to 180180^\circ.

Steps to Solve:

  1. In any triangle, the sum of the interior angles is always 180180^\circ.

  2. Given:

    • m1=20m\angle 1 = 20^\circ
    • m2=60m\angle 2 = 60^\circ
    • m3=xm\angle 3 = x (the third angle)

    The sum of the angles of the triangle will be: 20+60+x=18020^\circ + 60^\circ + x = 180^\circ

  3. Solve for xx: x=180(20+60)=18080=100x = 180^\circ - (20^\circ + 60^\circ) = 180^\circ - 80^\circ = 100^\circ

Thus, the value of xx is 100100^\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.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangle Angle Sum

Formulas

Sum of angles in a triangle: 180°

Theorems

Triangle Angle Sum Theorem

Suitable Grade Level

Grades 7-9