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Question

An isosceles triangle ABC has AC = BC. CD bisects AB at D and CAB=55. Then DCB equals



Your Answer
A
55
Correct Answer
B
35
Your Answer
C
70
Your Answer
D
75

Solution

The correct option is B 35

In ABC

AC = BC (given)

CAB=CBD   (Since angles opposite to equal sides are equal)

CBD=55

In ABC

CBA+CAB+ACB=180

But, CAB=CBD=55

ACB=1805555

i.e. ACB=70

Now, in ACD and BCD,

AC = BC   (given)

CD = CD  (common)

AD = BD  ( CD bisects AB)

ACDBCD   (By SSS congruence rule)

DCA=DCB  (c.p.c.t.)

DCB=ACB2=702

DCB=35

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