Math Problem Statement

Work out the value of x given the angles in a triangle as x, 2x, and 3x.

Solution

To solve this problem, we use the property of a triangle where the sum of the interior angles equals 180180^\circ.

The angles in this triangle are given as:

  • xx
  • 2x2x
  • 3x3x

Step 1: Set up the equation for the sum of the angles

x+2x+3x=180x + 2x + 3x = 180^\circ

Step 2: Simplify the equation

6x=1806x = 180^\circ

Step 3: Solve for xx

x=1806=30x = \frac{180^\circ}{6} = 30^\circ

Final Answer:

x=30x = 30^\circ

Would you like me to provide more detailed explanations or assist with a related topic? Here are 5 questions to deepen your understanding:

  1. What would the other angles of the triangle measure when x=30x = 30^\circ?
  2. How does the property of triangle angle sums apply in non-Euclidean geometry?
  3. What would change if the angles were expressed in terms of radians?
  4. How can you verify your solution using trigonometry?
  5. Could this problem be adapted for isosceles or right triangles?

Tip: Always verify the sum of your calculated angles equals 180180^\circ when solving for unknown angles in triangles.

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry
Triangle Angle Sum Property

Formulas

Sum of angles in a triangle = 180°

Theorems

Triangle Angle Sum Theorem

Suitable Grade Level

Grades 7-9