The ratio of the measures of the angles in a triangle is 2:9:4 what is the measure of the largest angle ?

You need to add all of these values together. This is 2 + 9 + 4 which gives 15

There are 180° in a triangle. Divide this by 15.

180/15 = 12

Then multiply this by the largest in the ratio; which is 9.

This is 12 x 9 which = 108°.

The largest angle is therefore 108°.

For reference, the ratio in degrees would look like this:

24:108:48, which adds up to 180°.