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 180Â°.
The sum of the three angles in any triangle is always equal to two right angles, or 180^{0}
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 × 180^{0 }
Sum of interior angles of a quadrilateral = 2 × 180^{0 }= (3 â€“ 2) × 180^{0 } = 360^{0}.
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 360^{0}.
Similarly, we can find the sum of exterior angles of Quadrilaterals.
Sum of exterior angles of Quadrilaterals is also 360^{0}.
In general,
Sum of exterior angles of n  sided polygon is 360^{0}.
Find the value of a.
We know that
Sum of interior angles of n  sided polygon is (n â€“ 2) × 180Â°
ž That is, sum of interior angles of quadrilateral is (4 â€“ 2) × 180Â° = 360Â°
ž 85Â° + 112Â° + 48Â° + a = 360Â°.
ž 245Â° + a = 360Â°
ž a = 360Â° − 245Â°
ž a = 115Â°.