Math Problem Statement

The angles of a triangle are in the ratio of 2:3:4. What is the degree measure of the largest angle?

Solution

The problem asks for the degree measure of the largest angle of a triangle where the angles are in the ratio of 2:3:4.

Step-by-step solution:

  1. Sum of Angles in a Triangle: The sum of the interior angles of any triangle is always 180180^\circ.

  2. Set Up the Equation Using the Given Ratio: Let the angles be represented as:

    • 2x2x, 3x3x, and 4x4x where xx is a common factor.

    The sum of these angles must equal 180180^\circ. Therefore, the equation is: 2x+3x+4x=1802x + 3x + 4x = 180^\circ Simplifying: 9x=1809x = 180^\circ

  3. Solve for xx: x=1809=20x = \frac{180^\circ}{9} = 20^\circ

  4. Find the Largest Angle: The largest angle corresponds to 4x4x: 4x=4×20=804x = 4 \times 20^\circ = 80^\circ

Thus, the largest angle is 80 degrees.

Would you like further details or clarifications?

Related Questions:

  1. What are the measures of the other two angles in the triangle?
  2. How would the solution change if the ratio was different, for example, 1:2:3?
  3. Why is the sum of a triangle's interior angles always 180°?
  4. Can a triangle have two angles in a 1:1 ratio?
  5. How would you calculate the angles if the triangle were not Euclidean, but spherical?

Tip:

Always remember to check that the sum of the angles in any triangle, regardless of the ratio, must add up to 180°.

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Math Problem Analysis

Mathematical Concepts

Geometry
Ratios

Formulas

Sum of angles in a triangle is 180°
Using ratios to solve for angles

Theorems

Triangle Sum Theorem

Suitable Grade Level

Grades 6-8