Worksheet on polygon angle sum theorem

Note: Sum of all angles of an n-sided polygon is given by =(n-2)×180 

Problem: 01 Find the angle measure of x 

Quadrilateral problems

Problem: 02 What is the sum of all angles of 

(i) a hexagon 

(ii) an octagon 

(iii) a regular 14 sided polygon 

Problem: 03 In the following figures, find the value of x.

(i) Quadrilateral problem (ii) Quadrilateral problem

Solution: 

 

Problem: 01 Find the angle measure of x 

Quadrilateral problems

Solution:

The given figure is a regular pentagon 

∴ Sum of all angle of pentagon =(n-2)×180=(5-2)×180=540º

Let each measured angle of the pentagon is xº

x+x+x+x+x=540º

5x=540º

x=108º

Thus, each angle measure of the pentagon is 108º

Problem: 02

02 What is the sum of all angles of 

(i) a hexagon 

(ii) an octagon 

(iii) a regular 14 sided polygon 

Solution: 

The sum of all angles of a polygon is given by (n-2)×180º where n number of side of polygon 

(i) We have a hexagon, that has 6 sides 

So, the sum of all angles of the hexagon is (6-2)×180º=(4)×180º=720º

(ii) An Octagon have 8 number of side

So, the sum of all angles of the octagon is (8-2)×180º=(6)×180º=1080º

(iii) The sum of all angles of a regular 14 sided polygon is given by (14-2)×180º=(12)×180º=2160º

Problem: 03 In the following figures, find the value of x 

Solution: 

(i) Quadrilateral problem We know, the sum of all angles of a quadrilateral is 360º

Now, we have 90º,90º,120º, and xº as four angles of the given quadrilateral 

∴  90º+90º+120º+xº=360º

300+x=360º

x=360º-300º=60º

Solution :

(ii) Quadrilateral worksheet We know, the sum of all angles of a parallelogram (quadrilateral) is 360º

∴ x + 60+x +120+60=360

2x+240=360

2x=360-240

2x=120 

x=60º

So, ∠A=60º   and ∠B=60+x=60+60=120º

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