How many sides does a regular polygon have if each of its interior angles is 165∘ With explanation
Answers
Answer:
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Hint: Here, we will first take the given angle of a regular polygon equal to 180∘(n−2)n
. Then we will simplify the obtained equation to find the value of n
.
Complete step-by-step answer:
We are given that each of the interior angles of a regular polygon is 165∘
.
Let us assume that the number of sides of a regular polygon is represented by n
.
We know that the measure of each interior angle of a regular polygon the formula is given by 180∘(n−2)n
.
Since the measure of each interior angle is 165∘
, we have
⇒180∘(n−2)n=165∘
Multiplying the above equation by n
on both sides, we get
⇒180∘(n−2)=165∘n⇒180∘n−360∘=165∘n
Adding the above equation with 360∘
on each side, we get
⇒180∘n−360∘+360∘=165∘n+360∘⇒180∘n=165∘n+360∘
Subtracting both sides by 165∘n
on both sides, we get
⇒180∘n−165∘n=165∘n+360∘−165∘n⇒15∘n=360∘
Dividing the above equation by 15∘
on each side, we get
⇒15∘n15∘=360∘15∘⇒n=24∘
Thus, the regular polygon with interior angle each measuring 165∘
is a 24-sided polygon.
Step-by-step explanation:
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