Question

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

= 55°

.

Find: (i) DCB (ii) CBD​

Answer 1

Answer:

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

= 55°

Answer 2

Answer:

Solution

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In ΔABC,

AC=BC [Given]

∴∠CAB=∠OBD [angle opp. to equal sides are equal]

⇒∠CBD+∠CAB+∠ACB=180

o

But⇒∠CAB+∠OBA=55

o

⇒55

o

+55

o

+∠AOB=180

o

⇒∠ACB=180

o

−110

o

⇒ACB=70

o

Now,

In ΔACD and ΔBCD,

AC=BC [Given]

CD=CD [Common]

AD=BD [Given:CD bisects AB]

∴ΔACD≅ΔBCD

⇒∠DCA=∠DCB

⇒∠DCB=

2

∠ACB

=

2

70

o

⇒∠DCB=35

o