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Properties of Polygons

Sum of Interior Angles :-
Measure the three angles of each triangle, with your protractor. Add up the measures. You will find that the sum is always 180°.

 




 

The sum of the three angles in any triangle is always equal to two right angles, or 1800

Now, let us see how many triangles are there in each polygon.
 

Polygons   Number of triangles
Quadrilaterals 2
Pentagon 3
Hexagon

 

4

 


Sum of interior angles of a polygon = Number of triangles in the polygon × 1800

Sum of interior angles of a quadrilateral = 2 × 1800 = (3 – 2) × 1800 = 3600.
 

In general, sum of interior angles of n - sided polygon is (n - 2) ´ 1800.

 

 

Sum of Exterior Angles
Now, let us discuss sum of exterior angles of polygons.

 


We have seen that sum of exterior angles of triangle is 3600.

Similarly, we can find the sum of exterior angles of Quadrilaterals.

Sum of exterior angles of Quadrilaterals is also 3600.

In general,

 

Sum of exterior angles of n - sided polygon is 3600.

 

Example

Find the value of a.

Solution

We know that

Sum of interior angles of n - sided polygon is (n – 2) × 180°

ž That is, sum of interior angles of quadrilateral is (4 – 2) × 180° = 360°

ž 85° + 112° + 48° + a = 360°.

ž 245° + a = 360°

ž a = 360°  245°

ž a = 115°.





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