Question

Find the value of the missing angle and then find x.

Answer 1

x=8

Explanation:

From the image, we can assume that the shape is a quadrilateral because it has 4 sides. A quadrilateral has 360 degrees in it. To start out, you need to find the measure of the inside angle. To get it, you would subtract 71 from 180 (since it is on a straight line) and get 109 degrees. From there, you just add all the angles up and set it equal to 360. If you add everything up, it should look something like 31x+112=360. You need to isolate x, so subtract 112 from both sides to get 31x=248. Now divide both sides by 31 and x should equal 8.

Answer 2

109°, x = 8

Explanation:

The angle inside the quadrilateral is adjacent to 71°, then

missing angle = 180° - 71° = 109°

The sum of the interior angles of a quadrilateral = 360°

sum the interior angles and equate to 360

8x - 1 + 13x - 2 + 10x + 6 + 109 = 360, that is

31x + 112 = 360 ( subtract 112 from both sides )

31x = 248 ( divide both sides by 31 )

x = 8