The measure of the supplement of an angle is three times the measure of the complement of the angle. How do you find the measures of the angles?

1 Answer

Answer:

Both angles are #45^@#

Explanation:

#m + n = 90#
as an angle and its complement equal 90

#m + 3n = 180 #

as an angle and its supplement equals 180

Subtracting both equations will eliminate m

#m + 3n -m - n= 180-90# this gives

#2n = 90# and dividing both sides by #2# gives

# 2n/2 = 90/2# so

#n = 45#

substituting #45# for #n# gives

#m + 45 = 90# subtracting #45# from both sides gives.

# m + 45 - 45 = 90 - 45 # so

#m = 45#

Both the angle and it complement are #45#

The supplement is #3 xx 45 = 135#