SOLUTION: Consider the following relationships among three angles: <1 is supplementary to <2 and complementary to <3, and <2 and <3 are a linear pair. Find m<1.

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Question 713726: Consider the following relationships among three angles: <1 is supplementary to <2 and complementary to <3, and <2 and <3 are a linear pair. Find m<1.
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
Start by writing what the problem tells you, and what you know.


What you know - the sum of supplementary angles is 180, the sum of complementary angles is 90, and the sum of linear pairs is 180.


What the problem tells you: m>1 + m>2 = 180, m>1 + m>3 = 90 and m>2 +m>3 = 180


There are three equations and three unknowns, so we can solve for all three.


Add the first two equations: m>1 + m>2 + m>1 + m>3 = 180+90 = 270.


We know, by the third equation, that m>2 + m>3 = 180, so substitute that into our added equations:


m>1 + 180 + m>1 = 270


Subtract 180 from both sides: 2*(m>1) = 90 ...divide by 2 m>1 = 45

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