Question

The sum of the exterior angles of any n-gon is 360˚. Find the sum of the interior angles of a 22-gon. Since the polygon has 22 sides, we can substitute this number for n: (n 2)180˚= (22 2)180˚= 20180˚= 3600˚.

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Answer 1

$\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3} }{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }& 1 & \sqrt{3} & \rm Not \: De fined \\ \\ \rm cosec A & \rm Not \: De fined & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm Not \: De fined \\ \\ \rm cot A & \rm Not \: De fined & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}}}$

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Answer 2

$\huge \bf \fbox \red{Answer}$

The sum of the interior angles of a regular polygon with n sides is 180(n-2). So, each interior angle has measure 180(n-2) / n. Each exterior angle is the supplement to an interior angle. Sum of exterior angles = n(360 / n) = 360.

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