Please solve q 80 ?

enter image source here

2 Answers
May 17, 2018

option (4) is acceptable.

Explanation:

enter image source here

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^@