Question

In the figure A=65°, ABC=56°

and BO, CO are the bisector of

angles ABC and BCA

respectively then find OCB and

BOC.​

Answer 1

Please see attachment first :D

GIVEN:

• Angle A=65°
• OB and OC are bisectors of angle B and C respectively.
• Angle ABC=56°

TO FIND:

• OCB
• BOC

SOLUTION:

As OB is bisector of angle B.

So:-

$\sf \large : \implies \: \: \angle OBC= \frac{56°}{2}=28°$

In triangle ABC by applying angle sum property

$\sf \large : \implies \: \: \angle A+ \angle B+ \angle C=180°$

$\sf \large : \implies \: \: 65 \degree+ 56 \degree+ \angle C=180°$

$\sf \large : \implies \: \: 121\degree+ \angle C=180°$

$\sf \large : \implies \: \: \angle C=180° - 121 \degree$

$\sf \large : \implies \: \: \angle C=59°$

$\large \sf : \implies \: \: \angle OCB= \frac{59}{2}$

$\large \sf : \implies \: \: \angle OCB= 29.5 \degree \: \: \huge\checkmark$

Now we have to find angle BOC

In triangle BOC by applying angle sum property

$\sf \large : \implies \: \: \angle OBC+ \angle OCB + \angle BOC=180°$

$\sf \large : \implies \: \: 28 \degree+ 29.5 \degree + \angle BOC=180°$

$\sf \large : \implies \: \: 57.5 \degree + \angle BOC=180°$

$\sf \large : \implies \: \: \angle BOC=180° - 57.5 \degree$

$\sf \large : \implies \: \: \angle BOC=122.5\degree \huge \checkmark$

Important property included is angle sum property.

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