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An equilateral triangle CDE is construct...

An equilateral triangle CDE is constructed on a side CD of sqaure ABCD. The measure of `angle AEB` can be __________.

A

`150^@`

B

`45^@`

C

`30^@`

D

`20^@`

Text Solution

Verified by Experts

The correct Answer is:
C

`angle ADE =angle ADC +angle CDE =90^@+60^@ (because "Angles in a square and equilateral triangle")=150^@`
In `Delta ADE, AD=DE`
`therefore angle DAE =angle DEA =(1)/(2)(180^@-150^@)`
Similarly, `angle CEB =15^@`
`therefore angle AEB=60^@-(angle DEA +angle CEB)`
`=60^@-(15^@+15^@)=30^@`.
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