SOLUTION: i'm having trouble finding m<1 . . . Given: <1 and <2 are supplementary <2 and <3 are supplementary <1= x^2+3y <2= 20y+3 <3= 3y+4x Find: m<1 (does not require proof)

Question 214848This question is from textbook Geometry for Enjoyment and Challenge
: i'm having trouble finding m<1 . . .
Given:
<1 and <2 are supplementary
<2 and <3 are supplementary
<1= x^2+3y
<2= 20y+3
<3= 3y+4x
Find: m<1
(does not require proof)
i've found x= -5.75+44.25, but i am confused on how to proceed ? how would you solve (-5.75+44.25)^2+3y+20y+3=180 ?
please help, thank you !!
This question is from textbook Geometry for Enjoyment and Challenge

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Using the fact that the sum of supplementary angles is 180 degrees, we can write two equations in x and y:
Substitute:

we get:
1). Similarly for angles 2 and 3.

Add the angles.
2). Simplifying 1). and 2). we have:
1a).
2a). Subtracting 2a) from 1a) we get:
3). Factor an x.
3a). so that:
or Substitute x = 0 into equation 1a) and solve for y.

or substitute x = 4 into equation 1a) and solve for y.

Subtract 19 from both sides.
Divide both sides by 23.

So angle 1 can have one of two measures:
Substitute x = 0 and y = 7.6957

degrees.

degrees.
or...
x=4 and y = 7.

degrees.

degrees.
As you can see, in both cases, the sums of angle 1 and angle 2 are 180 degrees.

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