Two angles are supplementary. One angle is 6 less than twice its supplement. What are the angles?

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Answer 1 · 2018-02-12T18:13:10

#62^@, 118^@#

supplementary angles add to #180^@#.

if one supplementary angle is denoted as #x#, then the angle #6# less than twice its supplement can be written as #2x - 6#.

adding them together, #x + 2x - 6 = 180#.

this can be solved algebraically.

#x + 2x - 6 = 180#

#3x - 6 = 180#

#3x - 6 = 3(x-2)#

#3(x-2) = 180#

#x - 2 = 60#

#x = 62#

the smaller angle is #62^@#.

the supplement to that, #2x - 6#, is #(124-6)^@#, which is #118^@#.

#62^@ + 118^@ = 180^@#.

therefore, the two angles, #62^@# and #118^@#, are supplementary.