Question

One angle in a triangle measures twice the smallest angle whereas the largest angle is six times the small angle. Find the measures of all three angles.

Answer 1

Use a variable (x) for the smallest angle (call it angle 1). Angle 1 = x The second angle is twice the smallest angle (2x) The largest angle is 6 times the smallest angle (6x) Take the sum of all three of those angles and make an equation,  equal to 180. x + 2x + 6x = 180 9x = 180  (combined like terms) x = 20  (divide by 6) Angle 1 (x) = 20 Angle 2 (2x) = 40 Angle 3 (6x) = 120

Answer 2

Let's say that x is the smallest angle. 
This equation could be used to solve for the smallest angle: 
x + 2x + 6x = 180 
There a 9x total in the equation equaling 180. 
Divide 180 by 9 to get 20, which is the measure of the smallest angle. 
One angle is twice that, which is 40. 
The biggest angle is 6 times that, which is 120. 
The three angles are 40º, 20º, and 120º. 
Hope this helps!