Two angles are supplementary. One angle is 5 degrees less than four times the other. What are the measures of the angles?

2 Answers
May 28, 2018

#a=143^o#, #b=37^o#

Explanation:

To be able to answer this, we must know what it means that the angles are supplementary. If you have two angles a and b and
#a+b=180^o#, they are supplementary.

As #a=4b-5^o#,
#a+b=4b-5^o + b=5b-5^o=180^o#
which gives #b=185^o/5=37^o#
Therefore #a=180^o - b= 143^o#

May 28, 2018

#color(blue)(143^@, 37^@)#

Explanation:

Let the angle be #theta#

One angle is 5 degrees less than four times the other.

One angle is #4theta-5#

The other angle is #theta#

Supplementary implies:

#4theta-5+theta=180=>theta=37#

So the angles are:

#4(37)-5=143^@#

#37^@#