Explanation

The sum of the interior angles of a polygon, use 180(n − 2), where n is the number of sides: Sum of the interior angles = 180(9 − 2) → 180(7) → 1260°.

Since this 9-sided figure is regular, all of the interior angles are equal: 1260° \(\div\) 9 = 140°.

Now we can find x:



x° + 140° = 180°

x = 40°


Hence the value 40 is correct.

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i think answer 15 is wrong. I found an answer 40

Thank you to point out. I had a mismatch posting the question.

yes, it is true. It is 40. Thank you once again.

regards
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isnt 360/n a simpler solution? 360/9=40

What's the theory behind your solution?

Points to remember:-

Sum of Interior Angles = (n-2) × 180° (n = number of sides)

Each Angle (of a Regular Polygon) = \(\frac{(n-2) * 180}{n}\)
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Attached is a visual that should help.

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Useful rule: the sum of the angles in an n-sided polygon = (n - 2)(180°)

So, the sum of the angles in an 9-sided polygon = (9 - 2)(180°) = 1260°

Since we have a REGULAR 9-sides polygon, each interior angle is EQUAL
1260°/9 = 140°
So, each interior angle is 140°


We get:



Since one of the 140° lies on the same line as angle x we know that the two angles add to 180°

We get" x° + 140° = 180°
Solve: x = 40°

Answer: 40

Cheers,
Brent
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I have a answer 40 but there is no box to insert it.

In the real test, you do have a box to insert your value for the correct answer.

Here, of course, on the board is not "the real test" on a computer. It is just a discussion.

When you attempt the question, you should start the timer, evaluate the question and solve for it and then, when you come to your value 40 or whatever it is, you push if your nailed it or pick it wrong.

So your workbook records it.

You can see the value, correct, under the spoiler tag.

Regards
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A quick look tells us that it's not likely that we're going to be able to solve for x directly, so let's figure out the interior angle.

We can draw 9 - 2 = 7 triangles from a given vertice. Each triangle is composed of 180 degrees. We also have 9 sides we want to divide the total number of degree. 180 * 7 / 9 = 20 * 7 = 140 = interior angle.

180 - 140 = 40.

So the answer is 40.

interior angle = n-2*180/n =(9-2) *180/9 =140
x=180-140 =40

Points to remember:-

Sum of Interior Angles = (n-2) × 180° (n = number of sides)

Each Angle (of a Regular Polygon) = (n−2)∗180n

i also used this method. anything wrong with it?

"The Exterior Angles of a Polygon add up to 360°. In other words the exterior angles add up to one full revolution." (applicable for any simple polygon)

To find quickly, single exterior angle = 360/n

You will get the result ,360/9=40

This is true for all type of regular polygons

40

If you don't want to remember a formula, it may be helpful to think of polygon angle totals as taking a triangle (180 degrees) and then adding 180 degrees for each additional side.

Bump
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