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?
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.
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.
To solve this problem, you can set up an equation based on the given information and then solve it using algebra. Let's go through the process step by step.
Let's call the measure of the smallest angle X. According to the problem, the medium-sized angle is 3 times the measure of the smallest angle, so the measure of the medium-sized angle is 3X. Additionally, it is given that the medium-sized angle is half the measure of the largest angle. We can represent the measure of the largest angle as 2 times the measure of the medium-sized angle, so the measure of the largest angle is 2(3X) = 6X.
Now, we know that the sum of the angles in a triangle is always 180 degrees. So, we can set up the equation:
X + 3X + 6X = 180
Simplifying, we have:
10X = 180
To find the value of X, we divide both sides of the equation by 10:
X = 180 / 10
X = 18
Now that we have the measure of the smallest angle, we can substitute it back into the expressions for the medium-sized and largest angles to find their values:
Medium-sized angle = 3X = 3 * 18 = 54 degrees
Largest angle = 6X = 6 * 18 = 108 degrees
So, the measures of the three angles are:
Smallest angle = 18 degrees
Medium-sized angle = 54 degrees
Largest angle = 108 degrees
To summarize, you can solve this problem by setting up an equation based on the given information and finding the value of X. Then, substitute X into the expressions for the medium-sized and largest angles to determine their values.