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In a triangle, if the angles are in ratio 2:3:5, what is the value of the largest angle?
90 degrees
80 degrees
100 degrees
70 degrees
90 degrees
Directly calculate the largest angle as 2+3+55×180°=90°.
The angles of the triangle are in the ratio 2:3:5, and the sum of angles in a triangle is 180 degrees.
Angle=(Sum of RatiosRatio)×180°
Directly calculate the largest angle as 2+3+55×180°=90°.
Students often fail to divide by the total sum of ratio parts (10) or incorrectly set the sum of angles to 360 degrees.
Set Up Ratio Equation
Let the angles of the triangle be 2x, 3x, and 5x. Since the sum of interior angles in a triangle is 180°, we set up the equation.
2x+3x+5x=180°
Simplify and Solve for x
Combine the terms on the left side to get 10x=180°, then solve for x.
x = \frac{180°{10} = 18°
Calculate the Largest Angle
The largest angle corresponds to the largest ratio part, which is 5. Multiply 5 by x.
5×18°=90°
A is correct because the largest angle of the triangle is calculated to be 90°.
Ratio-based division is a fundamental technique used heavily in partnership, mixtures, and polygon geometry problems.
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