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Question

ABCDE is a regular pentagon. If AD is joined, then

A
ABCD is a parallelogram
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B
ABCD is a rhombus
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C
ABCD is a cyclic
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D
ABCD is not a quadrilateral
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Solution

The correct option is C ABCD is a cyclic

In ΔAED,

E=1080 (Interior angle of pentagon)

EAD+EDA+LE=1080EAD=EDA(AE=ED)EAD=LEDA=360ABC=LEDC=1080
(Interior angle of pentagon)
EDC=ADC+LEDAADC=1080360=720ABC+ADC=108+72=1800
ABCD is cyclic since opposite angles add to 1800.

967802_924244_ans_3321521765434e909c0b635327eefd2c.png

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