The ratio of the measures of the three angles in a triangle is 2:9:4. Find the measures of the angles.

Step-by-step explanation:

If the angles exist in a ratio, that means that if you multiply each angle by the same number, they will still exist in that same ratio. We know that the angles of a triangle all add up to equal 180, so we can set up an equation using the numbers from the ratio and x as the unknown multiplier:

2x + 9x + 4x = 180 and

15x = 180 so

x = 12 ∴ (that means "therefore")

2x = 24,

9x = 108, and

4x = 48

Step-by-step explanation:

sum of ratio=2+9+4=15

1st angle=2/15*180=24°

2nd angle=9/15*180=108°

3rd angle=4/15*180=48°