Question

c) If each interior angle of a regular polygon is 144 degree , how many sides does this polygon
have?
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Answer 1

Answer:

Step-by-step explanation:

To find the no. of sides, we first need to find the measurement of the exterior angle.

Exterior angle  =  180  −  measurement of interior angle  =  180  −  144 =  36

To find the no. of sides, we use the formula  

⇒ 360

measurement of exterior angle

That is, no. of sides= 360 /36   = 10

Answer 2

Answer:

Number of Sides of Polygon = 10

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Step-by-step explanation:

Sum of Interior Angles = ( n - 2 ) × 180°

Each Interior Angle = [  ( n - 2 ) × 180° ] / n

144° =  [  ( n - 2 ) × 180° ] / n

144 n = 180n - 360

360 = 180n - 144n

360 = 36n

n = 360/36

n = 10