A triangular table has angles with measures in the ratio 7:9:4. What is the measure of the smallest angle?

The angles must add to 180 degrees.

Since the angles are in the ratio 7:9:4, their measures are not 7, 9, and 4 since 7, 9, and 4 do not add to 180. If you multiply 7, 9, and 4 by the same number, the new numbers will be in the same ratio. Since we do not know what that number is, we can use x for it.

Multiply 7, 9, and 4 by x to get

7x, 9x, and 4x.

Now add them and set equal to 180.

Then solve for x.

7x + 9x + 4x = 180

20x = 180

x = 9

Now that we know x equals 9, substitute x with 9 and evaluate 7x, 9x, and 4x to find the actual angle measures.

7x = 7 * 9 = 63

9x = 9 * 9 = 81

4x = 4 * 9 = 36

The angles measure 63, 81, and 36 degrees.