Posted by **Angie** on Saturday, April 14, 2012 at 7:48pm.

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?

- Algebra -
**Reiny**, Saturday, April 14, 2012 at 8:34pm
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.

- Algebra -
**Angie**, Saturday, April 14, 2012 at 8:56pm
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.

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