SOLUTION: the second angle of a triangle is 30 degrees less than the first angle. the third angle is twice the second angle. how large are the angles?
please and thank you
Algebra ->
Customizable Word Problem Solvers
-> Geometry
-> SOLUTION: the second angle of a triangle is 30 degrees less than the first angle. the third angle is twice the second angle. how large are the angles?
please and thank you
Log On
Question 153778: the second angle of a triangle is 30 degrees less than the first angle. the third angle is twice the second angle. how large are the angles?
please and thank you Answer by orca(409) (Show Source):
You can put this solution on YOUR website! let x be the measure of the first angle.
Then the second angle is x - 30, and the third angle is 2(x-30).
Their sum is x + (x - 30) + 2(x - 30)
As the three angles of any triangle add up to 180 degrees, we have:
x + (x - 30) + 2(x - 30)=180
Solving for x, we have:
x + x - 30 + 2x - 60 = 180
4x -90 = 180
4x = 270
x = 67.5
So
The first angle is 67.5 degrees
The second angle is x-30 = 67.5-30=37.5 degrees
The third is twice the second. so it is 2*37.5 = 75 degrees
(