The measure of the middle angle of a triangle is twice the smallest angle. The sum of the middle angle and the largest angle is 5 times the smallest angle. Find the measures of the angles.
+128408 Let the smallest angle = x the middle angle = 2x and the largest angle = y
And we have the following system
x + 2x + y = 180 (1)
5x = 2x + y ⇒ y = 5x - 2x ⇒ y = 3x (2)
Sub (2) into (1)
x + 2x + 3x = 180
6x =180
x = 180 / 6 = 30 = the smallest angle
2x = 60 = the middle angle
y = 3x = 90 = largest angle
