Question

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4. What is a regular polygon?

5. For a regular pentagon, (NOT MULTIPLE CHOICE),
a. Find the measure of a single interior angle.
b. Find the measure of a single exterior angle.

6. The measure of the interior angle of a regular polygon is 162°. How many sides does it have?

Answer 1

4. A regular polygon is a polygon that has all sides of equal length and all angles of equal measure. In other words, it is a polygon with both equal sides and equal angles.

5. For a regular pentagon:
a. The measure of a single interior angle can be found using the formula: (n - 2) * 180° / n, where n represents the number of sides of the polygon. For a pentagon, n = 5. Plugging the values into the formula:
Single interior angle = (5 - 2) * 180° / 5 = 3 * 180° / 5 = 540° / 5 = 108°

b. The measure of a single exterior angle in a regular polygon can be found by subtracting the measure of the corresponding interior angle from 180°.
Single exterior angle = 180° - Single interior angle = 180° - 108° = 72°

6. If the measure of the interior angle of a regular polygon is 162°, we can use the formula for the measure of a single interior angle: (n - 2) * 180° / n = 162°, where n represents the number of sides of the polygon.

Solving for n:
(n - 2) * 180° / n = 162°
Multiplying both sides by n:
(n - 2) * 180° = 162° * n
Distributing:
180°n - 360° = 162°n
Subtracting 180°n from both sides:
-360° = -18°n
Dividing both sides by -18°:
n = 20

Therefore, the regular polygon with an interior angle of 162° has 20 sides.



Star answer please ?

Answer 2

4.
A regular polygon is a polygon in which all sides are equal in length and all angles are equal in measure.

5.

a. The measure of a single interior angle in a regular pentagon is:
[(n – 2)*180°]/n = 540°/5 = 108°.

b. The measure of a single exterior angle in a regular pentagon is:
360°/n = 360°/5 = 72°.

6.
This can be found using the following formula:

[(n – 2)*180°]/n = Interior angle

(n-2)*180=162°*n

180n-360=162n

180n-162n=360

18n=360

n=360/18

n=20

where n is the number of sides in the regular polygon.

A regular polygon with an interior angle of 162° has 20 sides.