Question 1054022: If one angle of a triangle is equal to the sum of the other two show that the triangle is a right angle Found 2 solutions by ikleyn, josmiceli:Answer by ikleyn(52757) (Show Source):
Let "a" be the measure of the angle A;
Let "b" be the measure of the angle B;
Let "c" be the measure of the angle C.
Then
a + b + c = 180, (1)
a + b = c. (2) (given).
Add the equation (1) and (2). You will get
2(a+b) + c = 180 + c.
Simplify:
2(a+b) = 180 ---> a + b = = 90.
QED.
You can put this solution on YOUR website! Let the angles = , , and
(1)
The sum of the angles of a triangle
add up to degrees
----------------------------------
(2)
Use (1) to make the substitution:
(2)
(2)
(2)
and, from (1),
