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Question

# ABCD is a square and BCE is an equilateral triangle. Find the value of a,b and reflex ∠BED

A
20o,70o,230o
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B
18o,72o,210o
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C
15o,75o,225o
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D
25o,65o,210o
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Solution

## The correct option is C 15o,75o,225oABCD is a square and BCE is an equilateral triangle∠CEB=∠EBC=∠ECB=600Since ABCD is a square,∠DCB=900Now ∠DCB=∠DCE+∠ECB⇒900=∠DCB+600⇒∠DCE=300Now in triangle DCE,,EC=DC∴∠CDE=∠DEC=x (let)Again, ∠EDC+∠DEC+∠DCE=1800⇒x+x+360=180⇒2x=150⇒x=7560∴b=750Now, ∠ADC=900⇒∠ADE+∠EDC=900⇒a+750=900⇒a=150Now, reflex ∠BED=36060−∠BED⇒3600−(∠DEC+∠BEC)⇒3600−(750−600)⇒3600−13560⇒2250

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