PROBLEMS INVOLVING INTERIOR ANGLES OF A POLYGON WORKSHEET

Find the values of x in the following problems, giving brief reasons for your answers

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Problem 6 :

A regular polygon has interior angles of 156^o. How many sides does the polygon have?

Solution

Problem 7 :

Five identical isosceles triangles are put together to form a regular pentagon. 

a) Explain why 5x = 360.

b) Find x and y.

Solution

Problem 8 :

Find the measure of one interior angle in each polygon. 

Solution

Problem 9 :

Find the measure of one interior angle in each polygon. 

Solution

Problem 10 :

Find the measure of one interior angle in each polygon. 

Problem 11 :

Find the measure of one interior angle in each polygon. 

Solution

Problem 12 :

Find the measure of each exterior angle of a regular decagon. 

Solution

Problem 13 :

If the measure of each exterior angle of a regular pentagon is (2x + 4)°, find the value of x. 

Solution

Problem 14 :

Find the measure of each exterior angle of the regular polygon given below. 

Solution

Problem 15 :

Find the measure of exterior angle corresponding to the interior angle x° in the irregular polygon given below. 

Solution

Problem 16 :

In a polygon, the measure of each interior angle is (5x+90)° and exterior angle is (3x-6)°. How many sides does the polygon have ?

Solution

Answers :

(1)  x  =  108

(2)  x  =  150

(3)  x  =  60

(4)  x  =  150

(5)  x  =  95

(6)  15 sides.

(7)  x  =  72 and y  =  54

(8)   108°

(9)  135°

(10)  147° 3'

(11)   120°

(12)  x  =  34

(13)  40°

(14)  x  =  110

(15)  70°

(16)  12 sides. 

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