write the angle sum of a convex polygon with yhe number of sides given below a. 9 b. 10 ( give step by step answer)
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Maths > Understanding Quadrilaterals > Angle Sum Property of Polygons
Understanding Quadrilaterals
Angle Sum Property of Polygons
We already know that a simple closed curve that is made up of more than three line segments is called a polygon. Every polygon has a set of angles that are a result of the line segments involved in the closed figure. In the chapter below we shall learn about the angle sum property of polygons, which indirectly depends on the number of sides in that polygon.
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Questions
Two angles of a hexagon are
120
∘
and
160
∘
. If the remaining four angles are equal, find each equal angle.
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One angle of a seven-sided polygon is 114. and each of the other six angles is x
0
0
The value of x is
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Is it possible to have a polygon, whose sum of interior angles is
870
∘
Answer: No
State true or false:
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Angle Sum Property of Polygons
We have learned about the angle sum property in triangles! According to the angle sum property of a triangle, the sum of all the angles in a triangle is 180º. Since a triangle has three sides, we find the measurements of the angles accordingly.
Let’s recap the method. For example, if there is a triangle with angles 45º and 60º. The third angle is unknown. For finding the third angle we follow the given system of calculation:
A + B + C = 180º
A = 45º; B = 60º; C =?
45 + 60 + ? = 180º
? = 180º – 105º
? = 75º
So the third angle is 75º. Using the above-shown system of calculations we can find out the unknown angle in a triangle, but what about a polygon. Similarly, according to the angle sum property of a polygon, the sum of angles depends on the number of triangles in the polygon.
According to the Angle sum property of polygons, the sum of all the angles in a polygon is the multiple the number of triangles constituting the polygon. We use the angle sum property of triangles while calculating the unknown angles of a polygon.