Math Problem Statement
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:
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Sum of Angles in a Triangle: The sum of the interior angles of any triangle is always .
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Set Up the Equation Using the Given Ratio: Let the angles be represented as:
- , , and where is a common factor.
The sum of these angles must equal . Therefore, the equation is: Simplifying:
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Solve for :
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Find the Largest Angle: The largest angle corresponds to :
Thus, the largest angle is 80 degrees.
Would you like further details or clarifications?
Related Questions:
- What are the measures of the other two angles in the triangle?
- How would the solution change if the ratio was different, for example, 1:2:3?
- Why is the sum of a triangle's interior angles always 180°?
- Can a triangle have two angles in a 1:1 ratio?
- 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