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The angles of a triangle are in the ratio 3 : 1 : 2. Find the measure of the largest angle.
Given: The ratio of angles is 3 : 1 : 2.
To find: We have to find the measure of the largest angle.
Solution:
Let the common factor be = a
So,
1st angle = 3a
2nd angle = a
3rd angle = 2a
Now,
Sum of all angles of a triangle = 180o
3a + a + 2a = 180o
6a = 180o
a = 180o/6
a = 30o
Therefore,
1st angle = 3a = 3 x 30o = 90o
2nd angle = a = 30o
3rd angle = 2a = 2 x 30o = 60o
So, the largest angle is 90o.
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