SOLUTION: Hi! I was wondering if I have a triangle where two of the angles are 60 and the third angle is y and one side is labled 4x how would I find the variables? It also says the perimete

Click here to see ALL problems on Triangles

Question 708891: Hi! I was wondering if I have a triangle where two of the angles are 60 and the third angle is y and one side is labled 4x how would I find the variables? It also says the perimeter is 54 too.
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
All 3 angles in a triangle add up to 180 degrees, so

60+60+y = 180

120 + y = 180

y = 180 - 120

y = 60

So the third angle is 60

Since each angle is 60, we have an equilateral triangle. So we have 3 sides equal to 4x

They add to the perimeter of 54, which means

4x+4x+4x = 54

12x = 54

x = 54/12

x = 27/6

x = 9/2

x = 4.5

So in the end, x = 4.5 and y = 60

Because x = 4.5, each side is therefore 4.5*4 = 18 units long.

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

The sum of the measures of the angles of any triangle is 180 degrees. So if two of the angles are 60 degrees, the third one has to be 60 degrees as well creating an equiangular, and therefore equilateral, triangle.

If one of the sides of an equilateral triangle is 4x, then by definition, all three sides are 4x. The perimeter is the sum of the measures of the sides, so:

Solve for

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it