Question

If an exterior angle and an interior angle of a polygon are in ratio 2: 7,then the number of sides in the polygon is

Answer 1

Let 7a=interior angle
2a=exterior angle
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7a+2a=180
9a=180
a=20

So,
2a=40
7a=140
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For a regular polygon of n sides, each exterior angle has a measure of 360/n degrees.
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The measure of each interior angle is 140 degrees
Since the exterior angle of each angle has measure 40 degrees, then the number of sides n=360/40=9 sides.


I HOPE IT WILL HELP YOU
REGARDS

Answer 2

sᴏʟᴜᴛɪᴏɴ ⤵️

we know that sum of two interior and exterior angle=180°

therefore measure of the interior angle=7x

and measure of the exterior angle=2x

according to the question,

7x+2x=180

or,9x=180

or,x=180/9(dividing both sides by 9)

or,x=20(solution)

interior angle of the polygon=140°

exterior angle of the polygon=40°

now,we find the number of sides

formula for number of sides of polygon=360°/each exterior angle

therefore number of sides =360°/40°=9

diagonals of the polygon=n(n-3)/2

=9(9-3)/2

=54/2=27

☬polygon☬

In geometry, a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain or polygonal circuit. The solid plane region, the bounding circuit, or the two together, may becalled a polygon.