The measure of each interior angle of regular convex polygon is 156- - Find the number of sides of the polygon

The correct option is C 15 We know that, Sum of all the Internal angles of polygon =180 × (n 2) According to question, 180 × (n 2)=156 × n ⇒ 180 n 360^∘=156 n ...

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Standard VIII

Mathematics

Sum of Angles of a Polygon

The measure o...

Question

The measure of each interior angle of regular convex polygon is $156^{\circ}$ . Find the number of sides of the polygon

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Solution

The correct option is D
15

We know that,
Sum of all the Internal angles of polygon $= 180 \times (n - 2)$
According to question,
$180 \times (n - 2) = 156 \times n \Rightarrow 180 n - 360^{\circ} = 156 n \Rightarrow 180 n - 156 n = 360 24 n = 360 n = \frac{360}{24} = 15$

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The measure of each interior angle of regular convex polygon is 156∘ . Find the number of sides of the polygon

The correct option is D 15 We know that, Sum of all the Internal angles of polygon =180×(n−2) According to question, 180×(n−2)=156×n⇒180n−360∘=156n⇒180n−156n=36024n=360n=36024=15

The measure of each interior angle of regular convex polygon is $156^{\circ}$ . Find the number of sides of the polygon

The correct option is D
15

We know that,
Sum of all the Internal angles of polygon $= 180 \times (n - 2)$
According to question,
$180 \times (n - 2) = 156 \times n \Rightarrow 180 n - 360^{\circ} = 156 n \Rightarrow 180 n - 156 n = 360 24 n = 360 n = \frac{360}{24} = 15$