Please solve q 80 ?

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2 Answers
May 17, 2018

option (4) is acceptable.

Explanation:

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Given that, #AB=AC=BD# and #AC_|_BD#.

#rarrAB=AC#

#rarr/_B=/_C#

#rarr90-a+90-d=d#

#rarra=180-2d#.....[1]

Also, #rarrAB=BD#

#rarr/_A=/_D#

#rarra+b=90-b#

#rarra=90-2b#....[2]

From [1] and [2], we have,

#rarr180-2d=90-2b#

#rarrd-b=45#....[3]

Now, #/_C+/_D#

#=/_BCA+/_BDA=90-b+d=90+45=135#

May 19, 2018

#angleC+angleD=135^@#

Explanation:

enter image source here
Let #angleABD=x#,
given #AB=BD, => angleBDA=(180-x)/2#
let #angleCBD=y#,
given #AB=AC, => angleACB=angleABC=x+y#,
In #DeltaCBE, => color(red)(x+2y=90^@)#
#angleC+angleD=angleACB+angleBDA=x+y+(180-x)/2#
#=x+y+90-x/2#
#=x/2+y+90#
#=(x+2y)/2+90#
#=90/2+90=45+90=135^@#