$\vec{O A}, \vec{O B}, \vec{O C}$ are three rays in order that $A O B = 72 °, B O C = 26 °, \vec{O P} bisects A O C$ , then the value of $P O C$ is

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$59 °$

$48 °$

$49 °$

$39 °$

answer is A.

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Detailed Solution

$\begin{array}{l} A O C = A O B + B O C \\ = 72 ° + 26 ° = 98 ° \\ \vec{O P} bisects A O C \\ ∴ A O P = P O C \\ = \frac{1}{2} A O C \\ = \frac{1}{2} \times 98 ° \\ = 49 ° \end{array}$

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