The measure of the angles of a triangle are in a ratio of 2 : 3 : 4. Find the number of degrees in the smallest angle of the triangle.

Question

Please answer this ASAP!! I actually have no idea how to do this, and this is homework. I am in 8th grade geometry.

Answer 1

Remember the unstated constraint: the angles in a triangle in a plane add to 180 degrees.

 

We're looking for some u such that 

 

2u + 3u + 4u = 180

 

Then 9u = 180, u = 20.

 

What is the measure of the smallest angle in the triangle?

 

The key idea is that they are testing knowledge of the fact stated at the start of this solution. Then the test is to understand how to work with ratios. The other way to work with these ratios would be to let x be the smallest angle. Then 3 * x/2 is the measure of the next largest angle, and 4 * x/2 is the measure of the largest angle. Then these three add to 180, so you can solve for x.

Answer 2

Let the three angles' measurements be 2x, 3x & 4x for a total of 9x, thus x=20 so that the three angles total 180 deg.

The smallest angle must measure 40 deg.