SOLUTION: hi please help me i dont understand this problem in equilateral triangle DEF, Measure of angle D = x+y and measure of angle E = 2x-y please answer thanks a lott

Question 106400This question is from textbook
: hi please help me i dont understand this problem
in equilateral triangle DEF, Measure of angle D = x+y
and measure of angle E = 2x-y
please answer thanks a lott
This question is from textbook

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
In the equilateral triangle DEF, not only are the sides of equal lengths but the angles are equal to each other.
Since the sum of three angles of any triangle is 180 degrees, then each angle of the equialteral triangle DEF is 60 degrees.
Measure of angle D = x + y
The measure of angle E = 2x - y
But each of these angles is 60 degrees, so...
D = 60 degrees and E = 60 degrees, therefore:
1) x + y = 60
2) 2x - y = 60 Add equation 1) and 2) together (the y's are eliminated) to get:
3) 3x = 120 Divide both sides by 3.
4) x = 40 and, since:
x + y = 60, then y = 60 - x, so...
y = 60 - 40
y = 20
Answer: x = 40 and y = 20

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