Question

14) In a regular polygon, each interior angle is
four times the exterior angle. Find the
number of sides of the polygon.



The correct answer will be marked as brainliest..​

Answer 1

Answer:

you get interior angle = 4 * exterior angle = 4 * 36 = 144 degrees. 144 + 36 = 180 degrees so they are supplementary as required. the exterior angle of the regular polygon is equal to 360 / number of sides. solve for number of sides to get number of sides = 360 / exterior angle = 360 / 36 = 1

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Answer 2

$\huge{\boxed {\mathbb{QUESTION}}}$

In a regular polygon, each interior angle is

four times the exterior angle. Find the

number of sides of the polygon.

$\huge{\boxed {\mathbb {ANSWER}}}$

$Let\:exterior \:angle\:be\:x$

$Let\:interior \:angle\:be\:4x$

$\implies x+4x={180}^{\circ} (linear\:pair)$

$\implies5x={180}^{\circ}$

$\implies x=\frac{180}{5}$

$\implies{\boxed {x={36}^{\circ} }}$

$Sum \:of\:the\:angles \:in\:a\:polygon\:is\:{360}^{\circ}$

$\implies \frac{360}{x}$

$\implies \cancel \frac{360}{36}$

$\implies {\boxed {\boxed {{10}^{\circ} }}}$

$\huge{\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU }}}$

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$\huge{\boxed {\mathbb {EXTRA\:INFORMATION }}}$

$Linear\:pair={180}^{\circ}$

$Sum \:of\:the\:angles \:in\:a\:polygon\:is\:{360}^{\circ}$

$Area\: of \:rectangle =length \times breadth$

${\mathbb{\colorbox {orange} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {lime} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {aqua} {@suraj5070}}}}}}}}}}}}}}}$