Maths activity (1.to verify that the sum of interior angles of Aquadrilateral is 360 by paper cutting and pasting
2.to verify of sum of the measures of the exterior angle of any polygon is 360 by paper cutting and pasting give me my answer .
Answers
Answer:
the sum of interior angles of A quadrilateral is 360°
Sum of All exterior angle of polygon = 360°
Step-by-step explanation:
verify that the sum of interior angles of A quadrilateral is 360°
Let say ABCD is an Quadrilateral
Lets draw a line AC
now we have two triangles ΔABC & ΔCDA
As we know that sum of angles of a Triangle = 180°
in ΔABC ∠BAC + ∠ABC + ∠BCA = 180°
in ΔCDA ∠DAC + ∠CDA + ∠DCA = 180°
Adding both
∠BAC + ∠ABC + ∠BCA + ∠DAC + ∠CDA + ∠DCA = 180° + 180°
∠BAC + ∠DAC = ∠DAB
∠BCA + ∠CDA = ∠BCD
=> ∠ABC + ∠BCD + ∠CDA + ∠DAB = 360°
the sum of interior angles of A quadrilateral is 360°
verify of sum of the measures of the exterior angle of any polygon is 360°
A polygon have n sides & n vertices
Now at each vertices Interior Angle + exterior angle = 180° ( straight line)
Sum of All Interior Angle & exterior angle = n * 180°
Now i can draw n-2 triangles in a polygon starting from a point & completing all the vertices
Let say there are x1 , x2 , x3 ,..............................,xn-1 , xn vertices
Δx1 , x2 x3 , Δx1 , x3 , x4 , Δx1 , x4 , x5 Δx1 , xn-2 xn-1 , Δx1 , xn-12 xn
Total n-2 triangles
Sum of interior angles of all these triangles = (n-2) * 180°
= Sum of interior Angles of polygon = (n-2) * 180°
(n-2) * 180° + Sum of All exterior angle of polygon = n * 180°
=> Sum of All exterior angle of polygon = 2 * 180°
=> Sum of All exterior angle of polygon = 360°
Step-by-step explanation:
प्रोजेक्ट वर्क वेरीफाइड बाय पेपर कटिंग एंड पेस्टिंग