CBSE Class 9 Answered
Sum of the vertex angles of a five point star is 180degrees.How??Show the proof
Asked by Shivam Saxena | 12 Aug, 2010, 12:00: AM
Expert Answer
Dear Student
Here is a star
There is a pentagon in between and 5 triangles with vertices A,B,C,D and E
we have using angle sum property in all 5 triangles we have
A+(180-a)+(180-b) = 180
B+(180-b)+(180-c)=180
C+(180-c)+(180-d)=180
D+(180-e)+(180-d) =180
E+(180-e)+(180-f) =180
Adding the 5 equations we have
A+B+C+D + E +900 -2(a+b+c+d+e) = 0
A+B+C+D + E =540×2-900 = 180
we have using angle sum property in all 5 triangles we have
A+(180-a)+(180-b) = 180
B+(180-b)+(180-c)=180
C+(180-c)+(180-d)=180
D+(180-e)+(180-d) =180
E+(180-e)+(180-f) =180
Adding the 5 equations we have
A+B+C+D + E +900 -2(a+b+c+d+e) = 0
A+B+C+D + E =540×2-900 = 180
Regards
Team topperlearning
Answered by | 12 Aug, 2010, 09:55: PM
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