The easiest way to solve this is to use the exterior angles of the polygon. The sum of an exterior angle and interior angle is 180o. Also the sum of all the exterior angles of a polygon is 360o. As the polygon is regular, all the interior angles are the same and all the exterior angles are the same. So, for an interior angle of 172o the exterior angle is 180-172 = 8o. The sum of all the exterior angles is 360o so how many 8o make up 360o? 360/8=45. Thus the polygon with interior angles of 172o has 45 sides.
The name of a 172 sided polygon is ChiliHeptacontakaidigon.
Supplement of an angle measure x* be y*=(180-x*). Or x+y=180* for the problem x=9y => x+y = 9y+y=10y=180 => y=18* and x =172*
258
172
If you mean a regular polygon with each interior angle being 172 degrees then it will have 45 sides or a 45-agon
How many sides does a regular polygon have if the measure of each interior angle is equal to 172 degress ?
45
7740 degrees
No. If the interior angle is 8 degrees then each exterior angle must be 172 degrees. Therefore the polygon must have 360/172 approx 2.1 sides. A fractional side is not possible.
If one interior angle measures 172° then the corresponding exterior angle measures 180 - 172 = 8°. The number of sides = 360 ÷ 8 = 45.
The easiest way to solve this is to use the exterior angles of the polygon. The sum of an exterior angle and interior angle is 180o. Also the sum of all the exterior angles of a polygon is 360o. As the polygon is regular, all the interior angles are the same and all the exterior angles are the same. So, for an interior angle of 172o the exterior angle is 180-172 = 8o. The sum of all the exterior angles is 360o so how many 8o make up 360o? 360/8=45. Thus the polygon with interior angles of 172o has 45 sides.
20 sides because the supplement of 162 is 18. 18 is the measure of each exterior angle. the measure of all exterior angles=360. So 360/18=20.
Each interior angle of a regular 45-gon measures 172 degrees
A regular pentagon has 5 sides and each interior angle measures 108 degrees not 172 degrees
Exterior angle = 360/45 ie 8o so interior angles are 172o. Check: ((90 - 4) x 90)/45 = 86 x 2 = 172.
Interior angles of a 45-gon add up to 7740 degrees Each interior angle of a regular 45-gon measures 172 degrees