SOLUTION: Consider triangle ABC. It is given that AB = AC, AB = 4x + 2y, BC = 5x, and AC= 10y. is the triangle equilateral? Justify answer What is the smallest number that the su

Question 60684: Consider triangle ABC. It is given that AB = AC, AB = 4x + 2y, BC = 5x, and AC= 10y. is the triangle equilateral? Justify answer

What is the smallest number that the sum of the two largest angles in a scalene triangle can be if all the angle measures are whole numbers?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Consider triangle ABC. It is given that AB = AC, AB = 4x + 2y, BC = 5x, and AC= 10y. is the triangle equilateral? Justify answer
:
It may help to draw a triangle and label the sides as given:
:
Since AB = AC we can say:
:
4x + 2y = 10y
4x = 10y - 2y
4x = 8y
x = (8/4)y
x = 2y
:
If x = 2y and the third side, BC, is given as 5x, we can say:
5x = 5(2y) = 10y which is given as side AC, so it is, in fact, equilateral.
:
:
What is the smallest number that the sum of the two largest angles in a scalene triangle can be if all the angle measures are whole numbers?
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I guess that means that the 2 equal angles are both greater than the 3rd angle.
It would have to be close to being equilateral triangle (all angles 60 degrees)
I'm going to say angles of 61, 61, 58, smallest sum would be 122 degrees.
:
Let me know if I am wrong about this.
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