An irregular polygon has its external angles as 140 degree,120 degree,142 degree,132 degree,112 degree and x degree.find the value of x.

Question

Visualize an irregular polygon with five of its external angles visibly marked as 140 degrees, 120 degrees, 142 degrees, 132 degrees, and 112 degrees. The sixth angle, marked as x, should imply an unknown value. Include clear separations between the angles to emphasize their individuality. The colors should be vibrant and pleasing, with the polygon represented on a white background with a variety of color shades to highlight different angles. Make sure there is no text present in the image.

An irregular polygon has its external angles as 140 degree,120 degree,142 degree,132 degree,112 degree and x degree.find the value of x.

Answer 1

The exterior angles of a convex polygon add up to 360°

so since the given angles add up to more than that already, your polygon
is concave, so more information is needed. Perhaps some of those angles were
shown as negatives?

Answer 2

I don't understand

Answer 3

The sum of exterior angles of a convex polygon is always equal to 360 degrees. However, if the given exterior angles add up to more than 360 degrees, it means that the polygon is not convex, but concave. In a concave polygon, at least one of the interior angles is greater than 180 degrees. Therefore, more information is needed to determine the value of x, or to determine whether the given polygon is actually a concave polygon.

Answer 4

Well, looks like there's a party going on with some pretty unique angles! Now, let's see what we can derive from this polygon fiesta.

We know that the sum of the external angles of any polygon is always 360 degrees. So, if we add up all the external angles we have, we should get 360 degrees.

140 + 120 + 142 + 132 + 112 + x = 360

Now, let's add the numbers together: 646 + x = 360

Hmm, wait a second... 646 + x = 360? That doesn't seem right. It looks like our angles are definitely doing some crazy, mind-boggling acrobatics!

I suspect we've mixed up internal and external angles here. The internal angles of a polygon should add up to (n - 2) * 180 degrees, where n is the number of sides. But since we're given external angles, we'll need to subtract each angle from 180 degrees to find the corresponding internal angles.

So, let's do some handstands with math and calculate the internal angles:

180 - 140 + 180 - 120 + 180 - 142 + 180 - 132 + 180 - 112 + 180 - x = (6 - 2) * 180

Now let's simplify this equation: 900 - x = 4 * 180

And more simplification: 900 - x = 720

Now, let's get x all by itself: -x = 720 - 900 or -x = -180

Finally, we'll multiply both sides by -1 to solve for x: x = 180

Tada! The value of x is 180 degrees. So, our polygon is quite the regular joker, with x being the punchline!

Answer 5

To find the value of x, we need to know the sum of the external angles of any polygon. The sum of the external angles of any polygon is always 360 degrees.

In an irregular polygon, each external angle is different. So, we need to add up all the given external angles and subtract the sum from 360 degrees to find the missing external angle.

Let's calculate:

140 degrees + 120 degrees + 142 degrees + 132 degrees + 112 degrees + x degrees = 360 degrees

Now, let's solve for x:

646 degrees + x degrees = 360 degrees

Subtracting 646 from both sides:

x degrees = 360 degrees - 646 degrees

Simplifying:

x degrees = -286 degrees

So, the value of x is -286 degrees.