Question

the sum of the two angles of a triangle is equal to the third angle and the difference of the two angles is equal to two-thirds the third angle. find the measure of each angle

Answer 1

smallest angle --- x
middle sized -----y
largest ---------x+y

x + y + x+y = 180
x+y = 90 ***

x-y = (2/3)(x+y)
3x - 3y = 2x + 2y
x = 5y

sub into ***
5y + y = 90
y = 15
x = 75

smallest = 15
middle sized = 75
largest = 90