Find the number of sides of a regular polygon whose interior angle is 156 degrees

2 answers:

4 0

Find the number of sides of the regular polygon whose interior angles each measure 156 degrees
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Ext angle = 180 - Int angle = 24
n = 360/24 = 15 sides

Total interior angles = (n-2)*180
.
So, the average interior angle = ( (n-2)*180 ) / n
.
((n-2)*180)/n = 156
.
(n-2)*180 = 156n
180n -360 = 156n
24n = 360
n = 15
.
The polygon has 15 sides.

sergij07 [2.7K]3 years ago

3 0

Recall that the sum of the exterior angles is 360, and that an interior angle + an exterior angle = 180

Thus, if the interior angles are each 156, the exterior angles are each 180-156=24.

Now take 360/24 (because each exterior angle is 24 and they need to add to 360), you get 15. Thus, there are 15 sides.

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Find the area of the shaded region if the dimensions of the unshaded region are 18ft x 22ft . use 3.14 for π as necessary.

aivan3 [116]

The area of the shaded region in the given image is: 1,111.84 ft²

<h3>How to Find the Area of a Shaded Region?</h3>

To find the area of the shaded region in the image given, find the areas of the unshaded region, then subtract it from the total area of the whole figure.

Area of the total figure = area of two semicircles + area of the rectangle.

Dimensions of the rectangle is given as, 18ft x 22ft.

Area of the rectangle = 18ft × 22ft = 396 ft²

The diameter of each of the semicircle = 7 + 7 + 18 = 32 ft

The radius of each of the semicircle = 1/2(32) = 16 ft

Area of the two semicircles = 2(1/2 × πr²) = 2(1/2 × 3.14 × 16²)

Area of the two semicircles = 803.84 ft²

Area of the rectangle = 32 × 22 = 704 ft²

The total area = 704 + 803.84

The total area = 1,507.84 ft²

The area of the shaded region = 1,507.84 - 396

The area of the shaded region = 1,111.84 ft²