The measure of each interior angle of regular convex polygon is 145- - What is the number of sides of the polygon has-

The correct option is D 10We know that, Sum of all the Internal angles of polygon =180 × (n 2) According to question, 180 × (n 2)=144 × n ⇒ 180 n 360^∘=144 n ⇒ ...

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Standard VI

Mathematics

Regular Polygon and Its Properties

The measure o...

Question

The measure of each interior angle of regular convex polygon is $145^{\circ}$ . What is the number of sides of the polygon has?

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Solution

The correct option is D 10
We know that,
Sum of all the Internal angles of polygon $= 180 \times (n - 2)$
According to question,
$180 \times (n - 2) = 144 \times n \Rightarrow 180 n - 360^{\circ} = 144 n \Rightarrow 180 n - 144 n = 360 36 n = 360 n = \frac{360}{36} = 10$

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The measure of each interior angle of regular convex polygon is 145∘ . What is the number of sides of the polygon has?

The correct option is D 10We know that, Sum of all the Internal angles of polygon =180×(n−2) According to question, 180×(n−2)=144×n⇒180n−360∘=144n⇒180n−144n=36036n=360n=36036=10

The measure of each interior angle of regular convex polygon is $145^{\circ}$ . What is the number of sides of the polygon has?

The correct option is D 10
We know that,
Sum of all the Internal angles of polygon $= 180 \times (n - 2)$
According to question,
$180 \times (n - 2) = 144 \times n \Rightarrow 180 n - 360^{\circ} = 144 n \Rightarrow 180 n - 144 n = 360 36 n = 360 n = \frac{360}{36} = 10$