How to solve q 92 on the sides and angles of a polygon.?

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2 Answers

Hence the number of sides of the convex polygon is 15 and magnitude of the angle excluded is 150^@

Explanation:

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Let the actual number of sides of the polygon be n. So the sum of n interior angles will be (2n-4)*90^@
Now if x^@ be angle excluded to give the sum of (n-1) angles as 2190^@ As the polygon is convex one x<180^@

Hence we can write

(2n-4)xx90-x=2190

=>(180n-360)-x=2190

=>180n=(2190+360+x)

=>n=(2550+x)/180

=>n=(180*14+(30+x))/180

=>n=14+(30+x)/180

As n is a positive integer.Here it should be greater than 14. For x<180^@ Considering minimum value of (30+x)/180=1 we get x=150^@

Hence the number of sides of the convex polygon is 15 and magnitude of the angle excluded is 150^@

Mar 11, 2018

15 sides . Option C

Explanation:

A polygon can be divided into triangles by joining one vertex to all the others, The number of triangles will be:

"sum of interior angles"/(180°)

For example: (1080°)/(180°) = 6 triangles hArr 8 sides

In this case: (2190°)/(180°) = 12.167 triangles which is obviously not possible as the answer has to be a whole number.

The polygon is convex which means that the missing angle is not a reflex angle.

Therefore there must be 13 triangles which means 15 sides.

To find the size of the missing angle:

The sum of the interior angles will be:

13 xx180°= 2340°

The missing angle is 2340° -2190° = 150°