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Question

In the figure ABCD is a rectangle and DEC is an equilateral. Find DAE.
1378248_0c5a130a27784c44893d4ba07fdda92b.PNG

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Solution

ADE=90+60=150
BCE=90+60=150
In ADE and BCE
AD=BC(side of a square)
DE=CE(side of an equilateral triangle)
ADE=BCE
ADEBCE by SAS rule
AE=BE by CPCT
In ADE
AD=DE since AD=DC=DE
1=2
But 1+2+ADE=180 by angle sum property of
1+2+150=180
1+2=180150=30
1=2
21=22=30
1=2=302=15
DAE=15

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