Please solve q 96 ?

enter image source here

1 Answer
CW
May 11, 2018

BED=12^@BED=12∘

Explanation:

enter image source here
In BCE, angleBDC=180-78-24=78^@BCE,∠BDC=180−78−24=78∘
as angleBDC=angleDBC=78^@, => color(red)(CD=CB)∠BDC=∠DBC=78∘,⇒CD=CB
In DeltaBCE, angleBEC=180-51-78=51^@
as angleBEC=angleEBC=51^@, => color(red)(CE=CB)
=> CB=CD=CE
=> B,D and E are on a circle with center at C, as shown in the figure.
recall that the angle subtended at the center of a circle is twice the angle subtended at the edge from the same two points,
=> angleBCD=2angleBED,
=> angleBED=(angleBCD)/2=24/2=12^@

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