Answer:
b.12
Step-by-step explanation:
<u>Key skills needed: Interior Angle Measure Theorem, Equation Creation</u>
1) First, we need to classify this shape. It has 7 sides, which means that we can use the Interior angle Theorem to find out the sum of all the interior angle measures
The theorem is: ![S = (n - 2)180](https://tex.z-dn.net/?f=S%20%3D%20%28n%20-%202%29180)
S is the sum of all interior angle measures
n is the number of sides of the polygon
2) With this, we can plug in 7 for "n" (Since the figure has 7 sides) and get:
---> ![S = (7-2)180](https://tex.z-dn.net/?f=S%20%3D%20%287-2%29180)
---> (7-2) is 5 since 7 - 2 = 5 so --> ![S = 5(180)](https://tex.z-dn.net/?f=S%20%3D%205%28180%29)
---> 5(180) is the same as 5 x 180 which is 900 so --> ![S = 900](https://tex.z-dn.net/?f=S%20%3D%20900)
This means that the sum of all interior angles is 900 degrees.
3) Now, we have to find out the sum of all the angles that they gave us so:
---> ![10x + 10x + 9 + 133 + 9x + 14 + 12x - 9 + 10x + 5 + 136 = 900](https://tex.z-dn.net/?f=10x%20%2B%2010x%20%2B%209%20%2B%20133%20%2B%209x%20%2B%2014%20%2B%2012x%20-%209%20%2B%2010x%20%2B%205%20%2B%20136%20%3D%20900)
The left side is the sum of all interior angles in the shape, and the right side is what the sum should be when expressed as a number.
4) We have to combine all like terms on the left side:
---> ![10x + 10x + 9x + 12x + 10x = 51x](https://tex.z-dn.net/?f=10x%20%2B%2010x%20%2B%209x%20%2B%2012x%20%2B%2010x%20%3D%2051x)
--->
5) This means that ---> ![51x + 288 = 900](https://tex.z-dn.net/?f=51x%20%2B%20288%20%3D%20900)
Subtract 288 from both sides and get:
--->
(900-288 = 612)
Then divide by 51 from both sides and get:
--->
(612 ÷ 51 = 12)
Therefore b.12 is your answer.
<em>Hope you understood and have a nice day!! :D</em>