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In the diagram, PQR is a circle with center O. If ∠OPQ = 48^{o}, find the value of m

A. 96^{o}

B. 90^{o}

C. 68^{o}

D. 42^{o}

**Comments**

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PR is a straight line and the sum of angles on a straight line is 180.

Thus, m + ∠QOP = 180

∠QOP = 180 - m ----------- eqn(1)

Also, |OQP| is a triangle and the sum of all interior angles of a triangle is 180.

Thta is, ∠OPQ + ∠OQP + ∠QOP = 180

∠OPQ = 48

∠OPQ and ∠OQP are in the same segment and angles in a segment are always equal, thus, ∠OPQ = ∠OQP = 48

Therefore, 48 + 48 + ∠QOP = 180

from eqn(1), ∠QOP = 180 - m

48 + 48 + 180 - m = 180

276 - m = 180

m = 276 - 180

m = 96

**Ans A**

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