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 = 180^o  

3a + a + 2a = 180^o  

6a = 180^o  

a = 180^o/6 

a = 30^o  

Therefore,

1st angle = 3a = 3 x 30^o = 90^o   

2nd angle = a = 30^o  

3rd angle = 2a = 2 x 30^o = 60^o  

So, the largest angle is 90^o.