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Question
If the angles of a triangle are in the ratio 2 : 1 : 3, then find the measure of smallest angle.
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Solution
In the given problem, angles of ΔABC are in the ratio 2:1:3
We need to find the measure of the smallest angle.
Let,
∠A = 2x
∠B = x
∠C = 3x
According to the angle sum property of the triangle, in ΔABC, we get,
2x + 1x + 3x = 180°
6x = 180°
`x = (180°)/6`
x = 30°
Thus,
∠A - 2(30°) = 60
∠B = 1(30°) = 30
∠C = 3(30°) = 90°
Since, the measure of ∠Bis the smallest of all the three angles.
Therefore, the measure of the smallest angle is 30°.
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