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isosceles triangle:x+120+(2y+20)=180?

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3 Answers

This looks more complicated than it is.
Facts: An Isoscles triangle has 2 angles of the same measure.
Sum of the angles of a triangle = 180.

What's up with the chopped angle (2y + 20)?
It's distracting, just call it @. 

Look at your equation as:

x+120+@ = 180

because 2 angles have to be the same, either @ is 120 or @ is x.

@ is not 120, because 120+120=240 which is over 180. 
Foul ball.
So @=x
making the equation :

x+120+x=180
2x+120=180
2x=60
x=30

think back to your substitution
@ = x
so @ = 30
so your distracting, chopped angle 2y+20=30
2y=10
y=5

done. 
 

The sum of the 3 angles in the triangle is 180 degrees. We already know that an angle of the triangle  measures 120. In an isosceles triangle, two angles have the same measures and each of those two angles measures less than 90. This simply means that x=2y+20, when we do substitution,

we have x+120+x=180

           2x+120=180

           x=30

           y=(x-20)/2

            y=5

 

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