|
Question 887218: prove that the sum of three angles of a triangle is 180. using this result find x and all three angles if angles are {2x-1},{x-25}and{3x-10}
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! here's a proof that the sum of the interior angles of a triangle are equal to 180 degrees.
http://www.basic-mathematics.com/angle-sum-theorem.html
you basically construct a line passing through the vertex of one of the angles of the triangle and parallel to the opposite side.
this creates 2 parallel lines.
if the lines are parallel, then their alternate interior angles are equal.
this fact is then used to prove that the sum of the interior angles of the triangle have to be equal to 180 degrees.
your 3 angles are:
2x-1 and x-25 and 3x - 10
since the sum of the interior angles of a triangle are equal to 180 degrees, then:
2x-1 + x-25 + 3x-10 = 180
simplify this to get:
6x - 36 = 180
add 36 to both sides of this equation to get:
6x = 216
divide both sides of this equation by 6 to get x = 36
now that you know x, you can find your angles.
2x-1 = 2*36 - 1 = 72 - 1 = 71
x-25 = 36 - 25 = 11
3x-10 = 3*36-10 = 108-10 = 98
your 3 angles are 71 and 11 and 98
add them up and they total 180 degrees.
|
|
|
| |
