If each exterior angle of aregular polygon has a measure of x then how many sides does then polygon has
Answers
Answer:
We will use the formula Number of sides ×
Measure of each exterior angle =360∘
Step-by-step explanation:
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CBSE
Mathematics
Grade 9
Sum of the Measures of the Exterior...
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Related Questions
Find the number of sides of a regular polygon whose each exterior angle has a measure of
(i) 60∘
(ii) 72∘
.
Answer
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Hint: We will use the fact that the sum of the exterior angles of a polygon is 360∘
. We will substitute the given measures of angles in the formula and solve it further to get the required number of sides. A polygon is of different shapes made of straight lines and can be drawn on paper.
Formula used:
We will use the formula Number of sides ×
Measure of each exterior angle =360∘
.
Complete step-by-step answer:
Let the number of sides of the polygon be n
. It is given that the measure of each exterior angle of the polygon is 60∘
.
Using the formula, Number of sides ×
Measure of each exterior angle=360∘
, we get
n×60∘=360∘
Dividing both sides by 60∘
, we get
⇒n×60∘60∘=360∘60∘
⇒n=6
∴ The number of sides of a polygon with each exterior angle 60∘
is 6.
Let the number of sides of the polygon be n
. It is given that the measure of each exterior angle of the polygon is 72∘
.
Using the formula, Number of sides ×
Measure of each exterior angle=360∘
, we get
n×72∘=360∘
Dividing both sides by 72∘
, we get
⇒n×72∘72∘=360∘72∘
Thus, we get
n=5
∴ The number of sides of a polygon with each exterior angle 72∘
is 5.