Question

The angles of a triangle all add up to 180 degrees. If in a triangle, the measure of the largest angle 12 more than 5 times the measure of the smallest angle. The measure of the third angle is twice the measure of the smallest angle. What is the measure of the largest angle?

Answer 1

I got 21 for the smallest and 117 for the largest? is this correct?

Answer 2

if we use L (for largest), S (for smallest, and T (for third angle)
then they say:
largest angle is 12 more than 5 times the measure of the smallest angle.
L is 12 more than 5*S --> L = 12 + 5 S

third angle is twice the smallest angle
T = 2 * S

so we have
L = 12 + 5 S
T= 2S

the sum of the 3 angles is
L+S+T= 180

using our equations to replace L and T we write
12+5S + S + 2S = 180
or
8S +12 = 180
add -12 to both sides
8S = 168

divide both sides by 8
S= 21

and
L = 12 + 5*21 = 12+105 = 117