Question

The measure of the angles of a triangle are in extended ratio 2:2:8. What is the measure of the smallest angle?

Answer 1

what do the interior angles of a triangle add up to?

Answer 2

are the interior angles the 2s?

Answer 3

they're the 2, 2, and 8

Answer 4

ohhhh ok ok i see, it would be 12

Answer 5

they're a ratio. it doesn't mean that the angles are 2, 2, and 8 degrees

Answer 6

it means that the measure of the smallest if 4 times smaller than the largest

Answer 7

ok thats starting to make sense

Answer 8

so for example, let's do this with supplementary angles

the ratio of the larger angle to the smaller one is 8:1
together they're 9x so we can do 9x=180
x=20

Answer 9

and then plug it back into the ratio to figure out the angle measures. so 8*20=160
1*20=20

you can confirm they both add to 180

Answer 10

you have to do the same thing here with the triangle

Answer 11

\(2x+2x+8x=180\)

Answer 12

Ok that makes sense

Answer 13

thank you for your help!

Answer 14

anytime
post your answer when you're here if you want me to double check