Question

What is the value of x?

Answer 1

x = 8

Explanation:

With the outside angles known, we know the inside angles. Each angle on the outside in on a line so when added with the angle on the angle on the inside, it equals 180 degrees. We know 4 for sure so to save time, use this formula

(X * 180) - (All outside angles used)

X is the number angles used.

for us, it looks like this:

(4 * 180) - (59+77+66+62) = 456

456 is all the inside angles except for the angle beside 12x

subtract 456 from 540 because 540 is all the angles add to on a pentagon. we get 84.

This means 84 + 12x = 180 so we solve x

84 + 12x = 180

-84 -84

12x = 96

/12 /12

x =8

Answer 2

x = 8

Explanation:

The angles shown in the diagram are the external angles of the polygon.

The sum of the exterior angles of a polygon = 360°

Equate the sum of the angles to 360 and solve or x

62 + 66 + 77 + 59 + 12x = 360, that is

264 + 12x = 360 ( subtract 264 from both sides )

12x = 96 ( divide both sides by 12 )

x = 8