Question

The angle measures of the three angles of a triangle are in the ratio $1:3:6$. What is the number of degrees in the measure of the largest angle?

Answer 1

Because the angle measures are in the ratio 1:3:6, the angle measures are x, 3x, and 6x for some value of x. Because the angles of a triangle add to 18 degrees, we have x+3x+6x = 180 degrees, so 10x = 180 degrees and x =18 degrees. Therefore, the largest angle has measure 6x = 108.

Answer 2

Explanation:

Since the angles of a triangle all have to add up to equal 180, then, given the info we are given:

1x + 3x + 6x = 180 and

10x = 180 so

x = 18

That means that the smallest angle measures 18, the middle angle measures 3(18) which is 54, and the largest angle measures 6(18) which is 108.

Checking our math, does 18 + 54 + 108 add up to equal 180? Yes, it does!! Yay for us!!