Math Problem Statement

Doug needs to build an outside canopy for his daughter's playground. The angles in a diagram are listed as 2x, 3x, and 4x. What is the value of x?

Solution

To solve the problem, we are given three angles listed as 2x2x, 3x3x, and 4x4x. Since the angles form a triangle, the sum of the angles must be equal to 180°.

We can set up the equation as follows:

2x+3x+4x=180°2x + 3x + 4x = 180°

Simplifying:

9x=180°9x = 180°

Now, solve for xx:

x=180°9=20°x = \frac{180°}{9} = 20°

Thus, the value of xx is 20°. The correct answer is C. x=20x = 20^\circ.

Would you like more details or have any questions?

Here are some related questions to expand this topic:

  1. How do you determine the sum of angles in any polygon?
  2. What are the properties of a triangle with angles proportional to 2x2x, 3x3x, and 4x4x?
  3. Can you solve for xx in a triangle where angles are xx, 2x2x, and 3x3x?
  4. What is the formula to find interior angles of polygons with nn sides?
  5. How does this principle apply to non-Euclidean geometry?

Tip: When solving angle problems involving polygons, always remember that the sum of the interior angles of an nn-sided polygon is (n2)×180(n-2) \times 180^\circ.

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Math Problem Analysis

Mathematical Concepts

Geometry
Algebra

Formulas

Sum of interior angles in a triangle = 180°
2x + 3x + 4x = 180°

Theorems

Sum of angles in a triangle theorem

Suitable Grade Level

Grades 6-8