One angle of a triangle is 1/3 the largest angle, but twice the smallest. Find the largest angle.

Question

How to do the problem in step by step problems?

Answer 1

Many problems like this can be solved using the same method, and since this may be your actual homework question, I'm going to change numbers so that you can follow the process and get the answer yourself.

 

One angle of a triangle is 2/5 the largest, but 3 times the smallest angle. Find the middle angle.

 

You can set this up as a basic algebra problem.

 

There are 180 degrees in a triangle, and 3 angles. Those three angles are x for the smallest, 3x for the middle angle, and 3x/(2/5) for the largest. This is because the largest would be multiplied by (2/5) to get the middle, so dividing the middle by (2/5) will give you the largest.

 

Your equation would then be:

180=x+3x+(3/(2/5))x

180=(23/2)x

 

From here, you multiply each side by (2/23)

180(2/23)=(23/2)x*(2/23)

 

The right side of the equation cancels out the fractions, leaving x.

 

360/23=x

 

Since the middle angle is 3 times the smallest angle, x, you would multiply by 3.

 

360/23*3=1080/23≈47°

 

Answer 2

Sum of all angles of a triangle is 180.

Let's say that the smallest angle = x.

The middle angle is twice the smallest angle, so middle angle = 2x.

Middle angle is also 1/3 of the largest angle, so largest angle is 3 times the middle angle or largest angle = 3(2x) = 6x.

 

Small angle + Middle angle + Largest angle = 180

x + 2x + 6x = 180

9x = 180

x = 180/9 = 20

 

largest angle = 6x = 6(20) = 120