Question

please find this question

Answer 1

Now here is a triangle inside another triangle.
one triangle is ABC and the other is OCB
In triangle ABC , A+B+C= 180

in triangle OCB
BC is the common side.
<OBC = 1/2*<B
<OCB = 1/2*<C
1/2*B + 1/2*C + O = 180

O = 180 - (B+C)/2

from first triangle, B+C = 180- A

$o = 180 - \frac{(180 - a)}{2}$
$o = \frac{(360 - 180 + a)}{2}$
O = 90 + (A/2)

hence proved
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