Question

how many sides does a regular polygon have if each of its interior angle is 165 a)not possible b)12 c)15 d)24​

Answer 1

Given Interior angle = 165. = 24. Therefore the number of sides = 24.

Step-by-step explanation:

Given Interior angle = 165.

The measure of each exterior angle = 180 - 165

                                                             = 15

We know that sum of each exterior angles = 360

                                                                        = 360/15

                                                                        = 24.

Therefore the number of sides = 24.

Hope this helps!

Mark the brilliant

Answer 2

${\huge {\underline {\underline {\sf {Question}}}}}$

• How many sides does a regular polygon have if each of its interior angle is 165?

a)not possible

b)12

c)15

d)24

${\huge {\underline {\underline {\sf {Solution}}}}}$

• As we know , interior and the exterior angles make a linear pair

They add up to make 180°

• Now, then the measure of the exterior angle will be

= 180° - 165°

= 15°

• The sum of the exterior angles of polygon is 360°

• Then the values of exterior angle,

=360° ÷ 15°

= 24

●Do remind that, the number of exterior angles = the number of interior angles = the number of sides in polygon

Therefore there are 24 sides in this regular polygon so, option d)24 is correct.

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