In a regular pentagon ABCDE, draw
diagonal BE and then find the measure of :
(1) ZBAE (ii) ZABE (ii) ZBED
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Given:
- A Pentagon ABCDE
- a diagonal BE
To Find:
measure of :
↪∠BAE
↪∠ABE
↪∠BED
Solution:
1) Since number of sides in the Pentagon = 5
each exterior angle
∠BAE = 180° - 72°
2) in ∆ABE, AB = AE
∠ABE = ∠AEB
But ∠BAE + ∠ABE + ∠AEB = 180°
108° + 2∠ABE = 180° - 108° = 72°
∠ABE = 72°/2
3)Since,∠AED = 180° [∵ each interior angle = 180°]
∠AEB = 36°
∠BED = 108° - 36°
Hence:
∠BAE = 108°
∠ABE = 36°
∠BED = 72°
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ABCDE is a regular pentagon
sum of interior angles of polygon= ( N-2) × 180
here,
N= 5
therefore
(5-2)× 180
= 3× 180
= 540°
since all the 5 angles of a regular pentagon are equal measure , each angle is
540/5 = 108°
so angle BAE= 108°
In ∆ ABE ,
AB=AE
angle BAE+ angle AEB+ angle ABE =180°
108+ 2( ABE)= 180°
therefore,
angle ABE= 36°
Now,
Angle BED= 180°-108°=72.
hope it is useful for you
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