Answer: Angle C measures 132.5 degrees
Step-by-step explanation: What we have here is an irregular polygon with six sides. Two sides have been identified as 90 and 130. And the other sides are yet unknown. We shall start by computing the total sum of the interior angles of the six sided polygon.
The formulae for computing the interior angles of a polygon is given as (n - 2) x 180,
Where n stands for the number of sides of the polygon
Therefore in this diagram, sum of the interior angles equals
(6 - 2) x 180
= 4 x 180
= 720 degrees
That means the addition of all the given angles equals 720. This can be expressed as follows;
90 + 130 + (x + 10) + x + x + x = 720
220 + x + 10 + 3x = 720
By collecting like terms we now have
4x = 720 - 220 - 10
(Note that if a positive value crosses to the other side of an equation it becomes negative and vice versa)
4x = 490
Divide both sides of the equation by 4
x = 122.5
Therefore, since angle C is (x + 10)
C = 122.5 + 10
C = 132.5 degrees
