Step-by-step explanation: The formula that gives the measure of the interior angle of a regular polygon is: (n-2)*180/n, where n is the number of sides. The measure of one angle of the regular polygon whose number of sides is 18, is of 160 degrees.
Q. How many sides does a regular polygon have if the interior angle is 156?
15 sides
Q. How many sides does a 156 degree polygon have?
Q. How many sides does a regular polygon have if each of its interior angle is 155?
of 180-25 = 155 degrees. But you cannot have 2.32 sides. So you cannot have a regular polygon all of whose interior angle are 25 degrees.
Q. What is the measure of an interior angle in a regular polygon with 12 sides?
Dodecagon
| Regular dodecagon | |
|---|---|
| Coxeter diagram | |
| Symmetry group | Dihedral (D12), order 2×12 |
| Internal angle (degrees) | 150° |
| Dual polygon | Self |
Regular Polygons
| Sides | Name | Interior Angles |
|---|---|---|
| 17 | Heptdecagon | 158.82° |
| 18 | Octdecagon | 160.00° |
| 19 | Enneadecagon | 161.05° |
| 20 | Icosagon | 162.00° |
Q. What is the measure of an interior angle in a regular polygon with 18 sides?
Q. How do you find the measure of an interior angle of a regular polygon?
Lesson Summary A regular polygon is a flat shape whose sides are all equal and whose angles are all equal. The formula for finding the sum of the measure of the interior angles is (n – 2) * 180. To find the measure of one interior angle, we take that formula and divide by the number of sides n: (n – 2) * 180 / n.
Q. What is the measure of one interior angle of a regular polygon with 4n 2 sides?
That angle = 360/n where n is the number of sides. Then remember that the 2 base angles of the triangle making up the central angle and the two base angles = 180. 2b is the measure of the interior angle.
Q. What is the measure of each angle in a regular polygon with 9 sides?
The General Rule
| Shape | Sides | Each Angle |
|---|---|---|
| Octagon | 8 | 135° |
| Nonagon | 9 | 140° |
| … | … | … |
| Any Polygon | n | (n−2) × 180° / n |
