Question

Find the measure of the exterior angle at vertex C.

Answer 1

The sum of exterior angles is always 360, so to solve this one, you will have to add the exterior angles all up to find x:

10x + (4x + 26) + (12x + 44) + (7x - 3) + (6x + 59) = 360

39x + 126 = 360

39x = 234

x = 6

Now, the exterior angle at vertex C is 4x + 26.

Plug in the value you got for x:

4 * (6) + 26 = 50

The answer is 50 degrees.

Answer 2

Remark

The exterior angles of a convex polygon add up to 360o. Therefore for this pentagon, all 5 exterior angles = 360 degrees.

Equation

4x + 26 + 12x + 44 + 7x - 3 + 6x + 59 + 10x = 360 Combine like terms.

Solve

4x + 12x + 7x + 10x + 26 + 44 - 3 + 59 = 360

39x + 126 = 360 Subtract 126 from both sides.

39x = 360 - 126

39x = 234 Divide by 39

x = 234 / 39

x = 6

Answer

C = 4x + 26

C = 4*6 + 26

C = 24 + 26

C = 50