The ratio of the angles of a triangle is 3:7:2. What is the measure of the largest angle?

here's the solution,

let the given ratios as constants, by multiplying with same variable x

the angles will be 3x , 7x and 2x

now, we know the sum of the given angles measures 180°, since the sum of measures of all interior angles of a triangle is 180°

=》3x + 7x + 2x = 180°

=》12x = 180°

=》x = 15°

so, the measures of each angle is :

3x = 15 × 3 = 45°

7x = 15 × 7 = 105°

2x = 15 × 2 = 30°

and now, we can observe that the largest angle is 105°

the largest angle is 150°