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Question

In the given figure OBC and OKH are straight lines. If AH=AK,b=80andc=30 then the value of d is
327850_1b8645b7aa7548f98872be6db25aeb15.png

A
20
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B
25
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C
30
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D
45
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Solution

The correct option is B 25
In ABC
ACB=30o and ABC=80o.
BAC+ACB+ABC=180o
BAC+30o+80o=180o
BAC+110o=180o
BAC=70o
KAH=70o

In AHK,
AH=AK [ Given ]
AHK=AKH [ Base angles of equal sides are also equal ] ---- ( 1 )
KAH+AHK+AKH=180o.
70o+2AKH=180o.
2AKH=110o
AKH=55o.
AKH=BKO=55o. [ Vertically opposite angles ] ---- ( 2 )

ABC+ABO=180o [ Linear pair ]
80o+ABO=180o
ABO=100o
KBO=100o ---- ( 3 )

In BOK,
BOK+BKO+KBO=180o
d+55o+100o=180o [ From ( 2 ) and ( 3 ) ]
d+155o=180o
d=25o


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