Question

If < 1 and < 2 are supplementary angles in a ratio of 4:5.What is the measure of the smaller angle?

Answer 1

If < 1 and < 2 are supplementary angles in a ratio of 4:5.



What is the measure of the smaller angle?​

we have that

<1+<2=180 ------> equation A

<1/<2=4/5

<1=(4/5)<2 ------> equation B'

substitute equation B in equation A

(4/5)<2+<2=180

solve for <2

(9/5)<2=180

<2=180(5/9)

<2=100 degrees

that means

<1=80 degrees

therefore

the measure of the smaller angle is 80 degrees