Each interior angle of a regular polygon is 144 degrees Find the interior angle of a regular polygon which - Maths - Quadrilaterals

Question

Each interior angle of a regular polygon is 144 degrees Find the
interior angle of a regular polygon which has double the number of
sides as the first polygon

Lalit Mehra · Accepted Answer

Dear Student!

Let the number of sides of the given regular polygon be n.

Measure of each interior angle of the given regular polygon $= \frac{(n - 2) \times 180 °}{n}$

$∴ \frac{(n - 2) \times 180 °}{n} = 144 ° (Given) \Rightarrow \frac{n - 2}{n} = \frac{144 °}{180 °} = \frac{4}{5} \Rightarrow 5 n - 10 = 4 n \Rightarrow n = 10$

Number of sides of the other regular polygon = 2n = 2 × 10 = 20

Measure of each interior angle of the other polygon

$= \frac{(2 n - 2) \times 180 °}{2 n} = \frac{(20 - 2) \times 180 °}{20} = \frac{18 \times 180 °}{20} = 162 °$

Thus, the interior angle of the regular polygon which has double the number of sides of the given polygon is 162º.

Cheers!

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Each interior angle of a regular polygon is 144 degrees. Find the interior angle of a regular polygon which has double the number of sides as the first polygon.