# Algebra

posted by .

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 -

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 -

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.

## Similar Questions

1. ### Algebra

The measure of the largest angle of a certain triangle is 6 times the smallest. The measure of the remaining angle is 100 degrees less than te sum of the other two angles. Write a system of 3 equations you could use to solve this problem. …
2. ### Geometry

Find the smallest interior angle of equilateral if its exterior angle are in the ratio 2:3:4:6. PLEASE HELP..I DON'T KNOW HOW TO SOLVE THIS PROBLEM..THANKS
3. ### intermediate algebra

A triangle is such that the largest angle is 11 times the smallest angle. The third angle is 27° less than the largest angle. Find the measure of each angle. (Enter solutions from smallest to largest.)
4. ### intermediate algebra

A triangle is such that the largest angle is 11 times the smallest angle. The third angle is 27° less than the largest angle. Find the measure of each angle. (Enter solutions from smallest to largest.)
5. ### math

The sum of the 3 angles of a triangle is 180 degrees. In triangle PQR, the largest angle is twice the size of the smallest angle. The remaining angle is 16 degrees larger than the smallest. Write and solve an equation to find the size …
6. ### geometry

I can't figure out this problem, help would be much appreciated! Suppose line BC bisects angle ABE, and D is the interior of angle ABC. If m-angle CBD=28 degrees, and m-angle ABE=136 degrees, find m-ABD.
7. ### Algebra II

The measure of the largest angle of a triangle is 90 more than the measure of the smallest angle, and the measure of the remaining angle is 30 more than the measure of the smallest angle. Find the measure of each angle. Show your …
8. ### algebra

A triangle is such that the largest angle is 12 times the smallest angle. The third angle is 20 less than the largest angle. Find the measure of each angle. (12-x)+ x+20-(12-x)=180. im having a difficult time setting up the equation
9. ### Algebra

One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 10 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
10. ### Algebra

One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 10 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.

More Similar Questions