✒️[tex]\large{\mathcal{ANSWER}}[/tex]
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The sum of the internal angles of this polygon is 540°, and the value of the unknown x is 130.
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● But how do you know this?
- We can arrive at these results from the formula for the sum of the internal angles of a convex polygon.
● And what formula is this?
[tex] \: \boxed{Si = (n - 2).180} [/tex]
● Where:
- Si = sum of internal angles.
- n = Number of sides of the polygon.
Knowing this formula, we can solve the question:
- It asks us to calculate the sum of the polygon in the figure, if we analyze the figure well, we realize that this polygon is called a pentagon, that's because it has 5 sides, so we have already figured out our "n" in the formula. With that , we can find the sum of the internal angles , because by the formula , we have to :
[tex]Si = (5 - 2).80° \\ Si = 3.80° \\ \: \boxed{Si = 540°} [/tex]
● How do we go about figuring out the value of x ?
- Notice , we're going to set up a first degree equation , to figure out the value of x , we're just going to equate all the inside angles of the polygon to 540°, doing that , we have to :
[tex]x + x + x + 75 + 75 = 540 \\ 3x + 150 = 540 \\ 3x = 540 - 150 \\ 3x = 390 \\ x = \frac{390}{3} \\ \: \boxed{x = 130°} [/tex]
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Good studies and I hope I have helped.
