Question

Find the value of x.
a.17
b.12
c.40
d.18
e.none are correct

Answer 1

b.12

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:
`S = (n - 2)180`

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`

---> (7-2) is 5 since 7 - 2 = 5 so -->
`S = 5(180)`

---> 5(180) is the same as 5 x 180 which is 900 so -->
`S = 900`

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`

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`

--->
`9 + 133 + 14 -9+5+136 = 288`

5) This means that --->
`51x + 288 = 900`

Subtract 288 from both sides and get:

--->
`51x = 612` (900-288 = 612)

Then divide by 51 from both sides and get:

--->
`x = 12` (612 ÷ 51 = 12)

Therefore b.12 is your answer.

Hope you understood and have a nice day!! :D