Question

The interior angle of a regular polygon exceeds its exterior angle by 108°.
Find:
i) The measure of each interior angle
ii) The measure of each exterior angle
iii) Number of sides in polygon

Answer 1

Answer:

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Step-by-step explanation:

In a polygon of n sides , if we join all vertices with a point inside it , then n number of triangles will formed . Total inside angles of all the triangles are n×180° .This total angles includs sum of all interior angles of the polygon and angle 360° arround the inside point .

measurment of one inside angle of the polygon of n sides is 108°

Total inside angles of the polygon=n×108°

So we can write n×108+360=n×180

or n(180–108)=360

or, n×72=360

or, n=360/72=5

so number of sides =5