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The interior angles of a triangle are in the ratio 2:3:5. What is the measure of the largest angle?
72 degrees
90 degrees
108 degrees
80 degrees
90 degrees
Sum of ratios is 2 + 3 + 5 = 10 parts, which equals 180 degrees. Since the largest part is 5 (half of 10), the largest angle is half of 180 degrees, which is 90 degrees.
Ratio of interior angles of a triangle = 2:3:5
Largest┬аAngle=2+3+55тАЛ├Ч180┬░
Sum of ratios is 2 + 3 + 5 = 10 parts, which equals 180 degrees. Since the largest part is 5 (half of 10), the largest angle is half of 180 degrees, which is 90 degrees.
Students often forget to divide by the total sum of the ratio parts and instead multiply the ratio directly by 180 degrees.
Understand the Ratio of Angles
Let the interior angles of the triangle be 2x, 3x, and 5x based on the given ratio 2:3:5.
2x+3x+5x=180┬░
Apply Triangle Angle Sum Property
The sum of all interior angles in a triangle is always 180┬░. Add the algebraic parts together to solve for x.
10x=180┬░
Find the Value of x
Divide both sides by 10 to find the multiplier x.
x = \frac{180┬░{10} = 18┬░
Calculate the Largest Angle
Substitute x back into the largest angle part of the ratio, which is 5x.
Largest┬аAngle=5├Ч18┬░=90┬░
B is correct because the largest angle corresponding to the ratio part 5 calculates to exactly 90 degrees.
Ratio division principles are frequently used in polygon angle sums, mixture problems, and work-time efficiencies in RRB exams.
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