Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

A regular polygon has angles of size 150 degrees each. How many sides does the polygon have?

Answer
VerifiedVerified
479.7k+ views
like imagedislike image
Hint: We will look at the definition of a regular polygon. We will see some examples of regular polygons and also the properties of a regular polygon. We will find the measure of the exterior angle using the given measure of the interior angle. We will use the property of the exterior angles of a regular polygon to find the number of sides of the regular polygon.

Complete step by step answer:
A regular polygon is defined as a polygon that has all the sides of equal length and all the angles of the same measure. An equilateral triangle is a regular polygon that has three sides. A square is a regular polygon that has four sides.
In a regular polygon, the sum of an interior angle and its exterior angle is 180. We will use this property to find the measure of the exterior angle of the regular polygon given in the question. Its interior angle has measure 150. Therefore, the exterior angle has measure 180150=30.
Regular polygons have the property that the sum of all its exterior angles is 360. Using this property, we can see that
number of sides=sum of exterior anglesmeasure of one exterior angle
Substituting the respective values, we get the following,
number of sides=360 30number of sides=12
Therefore, the number of sides of the regular polygon with interior angle 150 is 12. This regular polygon looks like the following,
seo images


Note: The sum of the interior angles of this regular polygon will be 150×12=1800. It is useful to know the relation between the interior angles, the exterior angles and the number of sides of a regular polygon. There is a formula to find the sum of interior angles of a polygon using the number of sides. This formula uses the fact that we can divide a regular polygon into triangles.
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
calendar iconAcademic year 2025-26
language iconENGLISH
book iconUnlimited access till final school exam
tick
School Full course for CBSE students
PhysicsPhysics
ChemistryChemistry
MathsMaths
₹41,848 per year
Select and buy