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Question

In the given figure, x = ?
(a) α + β − γ
(b) α − β + γ
(c) α + β + γ
(d) α + γ − β

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Solution

(c) α + β + γ

Join OC to produce it to D.
Let BOC=m°, AOC=n°, BCD=p° and ADC=q°.
Then, m+n=β and p+q=x.
Side OC of triangle BOC is produced to D.
p=α+m ...i
Side OC of triangle AOC is produced to D.
q=n+γ ...ii
Adding (i) and (ii), we get:p+q=α+γ+m+nx=α+β+γ

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