24. For getting diagonals through vertex A of a pentagon ABCDE, A is joined to which points?
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Answer:
(A)can be joined with c or d
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In a regular pentagon ABCDE, draw a diagonal BE and then find the measure of ∠BED
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Correct option is
A
72
∘
In a regular pentagon ABCDE, BE is a diagonal.
∠BAE is the interior angle of the polygon.
Each interior angle of a regular polygon is =
n
180
o
(n−2)
where n= number of sides of polygon, n=5
∠BAE=
5
180
o
(5−2)
=108
o
So, each angle of polygon is 108
o
also ∠AED=108
o
Now, △ABE is an isosceles triangle in which AB = AE.
So, ∠ABE=∠AEB
∠ABE+∠AEB+∠BAE=180
o
=>2∠AEB=180
o
−108
o
=>∠AEB=
2
72
o
=36
o
∠BED=∠AED−∠AEB=108
o
−36
o
∠BED=72
o
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