One angle is 12 more than twice its supplement. What is the measure of both angles?

1 Answer
Dec 20, 2017

See a solution process below:

Explanation:

Let's call the first angle #alpha#.

Supplementary Angles are angles which add up to #180^o#

Therefore, the Supplementary Angle to #alpha# is:

#180^o - alpha#

Twice this is:

#2(180^o - alpha)#

Then 12 more than this is:

#2(180^o - alpha) + 12^o#

Then the measure of both these angles would be:

#alpha + 2(180^o - alpha) + 12^o#

Simplifying gives:

#alpha + (2 xx 180^o) - (2 xx alpha) + 12^o#

#alpha + 360^o - 2alpha + 12^o#

#360^o + 12^o + alpha - 2alpha#

#372^o + 1alpha - 2alpha#

#372^o + (1 - 2)alpha#

#372^o + (-1)alpha#

#372^o - 1alpha#

#372^o - alpha#