5. The measures of angles of hexagon are 4x, 5x, 6x, 7x, 8x and 9x. Calculate the size of the largest angle

166 2/13 deg

Step-by-step explanation:

The sum of the measures of the interior angles of a convex polygon of n sides is 180 (n - 2).

A hexagon has 6 sides, so n = 6.

sum of measures of angles = 180 (n - 2) = 180 (6 - 2) = 180 (4) = 720

4x + 5x + 6x + 7x + 8x + 9x = 720

39x = 720

x = 720/39

x = 240/13

The largest angle has measure 9x.

9x = 9 * 240/13 = 2160/13

2160/13 = 166 2/13

Answer: 166 2/13 deg