The following problem must be solved 3 different ways in which X=smallest angle for problem 1. Problem 2 would be X=medium sized angle. Problem 3 would start with X=largest angle. I was able to figure out X=smallest angle, but I am stumped on the other 2 as to how to set it up.

Question

The following problem must be solved 3 different ways in which X=smallest angle for problem 1.  Problem 2 would be X=medium sized angle.  Problem 3 would start with X=largest angle.  I was able to figure out X=smallest angle, but I am stumped on the other 2 as to how to set it up.

In a triangle the measure of the medium-sized angle is 3 times the measure of the smallest angle and half the measure of the largest angle.  What are the measures of the 3 angles?

Reiny · Answer

I will do the first, and start you off on the second

method1:
smallest angle -- x
medium-sized angle -- 3x
larges angle --- 6x

x + 3x + 6x = 180
10x = 180
x = 18
3x = 54
6x = 108 , not 108+54+18 = 180

method 2:
medium sized angle = x
small angle = (1/3)x
large angle = 2x

x + (1/3)x + 2x = 180
multiply by 3
3x + x + 6x = 540
10x = 540
x = 54
(1/3)x = 18
2x = 108 , notice we got the same answers

you do the 3rd way.

Angie · Answer

Reiny...yes, thank you. I appreciate the help so much. I did have the some work-up for X=smallest angle. Thanks for starting me out for the next 2 angles.