The measures of the angles of a triangle are in the ratio of 1 : 2 : 3. Find the degree measure of each angle.

Answer 1

Hi Darrien,

For this question, it requires that we remember a fact about triangles: the sum of the interior angles of a triangle will always add up to 180 degrees.

We also need to know how to deal with a ratio with more than two terms. When dealing with a ratio of more than two parts, I like to think of each of the numbers in the ratio as parts of a whole. So for the ratio 1:2:3, there are 6 parts total (1 + 2 + 3), and the 1 represents 1 part out of 6 parts (or 1/6), the 2 represents 2 parts out of 6 (2/6), and the 3 represents 3 parts out of 6 (3/6).

Now we know that the sum of all the angles of a triangle add up to 180 and that there are 6 parts in the whole ratio. So if 6 parts is 180 degrees, 1 part would be 30 degrees. That means the angles would be 30, 60, and 90 degrees (1 part, 2 parts, and 3 parts, respectively).

Hope this makes sense! I find that a lot of students get confused by ratios of more than two terms, so take some time to think about it and make sure you get it.