Question 19326: find the measure of an angle that is two-thirds of its supplement.
A. 36 degree B. 54 degree C. 72 degree D. 108 degree
Answer by mmm4444bot(95)   (Show Source):
You can put this solution on YOUR website! Hello There:
First off, we need to know what the definition of a supplementary angle.
When you have an angle that is less than 180 degrees, then the supplement is the angle that gives you a total of 180 degrees if you add it to your angle.
Let me explain that in a different way with some examples.
If the angle is 100 degrees, then the supplement is 80 degrees because 100 + 80 = 180 degrees.
If the angle is 45 degrees, then the supplement is 135 degrees because 45 + 135 = 180 degrees.
In other words, if you're given an angle that is less than 180 degrees, you find that angle's supplement by subtracting it from 180 degrees.
Let choose the variable name x to represent our unknown angle.
If x is the angle, then 180 - x is the supplement.
Two-thirds of the supplement can be expressed as (2/3)*(180 - x).
(The asterisk means multiplication.)
This is enough information to write an equation.
x = (2/3)*(180 - x)
x = (2/3)*180 - (2/3)*x
x = 120 - (2/3)*x
x + (2/3)*x = 120
(5/3)*x = 120
x = (3/5)*120
x = 72
Let's check our result.
The supplement to 72 degrees is 180 - 72 = 108 degrees. Two-thirds of 108 is 72. Our result checks out.
The answer is 72 degrees.
~ Mark
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