The measure of the supplement of an angle is 20° more than three times the measure of the original angle. What are the measures of the angles?

1 Answer
Feb 27, 2017

The original angle is #40^@#.
Its supplement is #140^@#

Explanation:

Recall that the sum of supplemental angles is #180^@#.

Based on the question, an expression can be set up with a variable.

If #x# is the value of the original angle, and #(3x+20)# is equal to its supplement, then
#180=x+(3x+20)#

Solving for x, we get:
#180=4x+20#

#160=4x#

#40=x#

The original angle is #40^@#.

To find the supplement, plug in 40 to the expression that we defined above. The supplement is equal to:
#=3*(40)+20#

#=120 + 20=140#

Its supplement is #140^@#

To check, verify that the two angle measurements meet the definition, meaning they sum to #180^@#

#140^@+40^@=180^@#