Question

In the figure , equilateral triangle EDC surmount on a square ABCD. If angle DEB=x degree, find the value of x

Answer 1

Answer:

angle x = 45°

dc = bc = ce

so Δbce is isosceles

and ∠ecb  = ∠ecd + ∠bcd

=> ∠ECD = 60 + 90 = 150

and ∠cbe + ∠ceb + ∠bce = 180 [ note ∠cbe = ∠ceb]

=> 2∠ceb + ∠bce = 180

=> 2∠ceb + 150 = 180

=> 2∠ceb = 180 - 150 = 30

=> ∠ceb = 30/2 = 15°

now ∠dec = 60° ...............(i)

and ∠dec = ∠ceb + ∠deb ...............(ii)

by (i)&(ii) we get

=> 60 = x° + 15°

=> x = 60 - 15

=> x = 45°

Answer 2

Answer:

x= 45⁰

Step-by-step explanation:

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