Answer:
b.12
Step-by-step explanation:
Key skills needed: Interior Angle Measure Theorem, Equation Creation
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: [tex]S = (n - 2)180[/tex]
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:
---> [tex]S = (7-2)180[/tex]
---> (7-2) is 5 since 7 - 2 = 5 so --> [tex]S = 5(180)[/tex]
---> 5(180) is the same as 5 x 180 which is 900 so --> [tex]S = 900[/tex]
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:
---> [tex]10x + 10x + 9 + 133 + 9x + 14 + 12x - 9 + 10x + 5 + 136 = 900[/tex]
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:
---> [tex]10x + 10x + 9x + 12x + 10x = 51x[/tex]
---> [tex]9 + 133 + 14 -9+5+136 = 288[/tex]
5) This means that ---> [tex]51x + 288 = 900[/tex]
Subtract 288 from both sides and get:
---> [tex]51x = 612[/tex] (900-288 = 612)
Then divide by 51 from both sides and get:
---> [tex]x = 12[/tex] (612 ÷ 51 = 12)
Therefore b.12 is your answer.
Hope you understood and have a nice day!! :D
