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In the following figure if \( \Large \angle BOC \) = \( \Large 7x ^{\circ} + 20 ^{\circ} \) and \( \Large \angle COA \) = \( \Large 3x ^{\circ} \), then value of x for which \( \Large \angle AOB \) becomes a straight line is

A) \( \Large 16 ^{\circ} \)
B) \( \Large 14 ^{\circ} \)
C) \( \Large 20 ^{\circ} \)
D) \( \Large 21 ^{\circ} \)

Correct Answer:

A) \( \Large 16 ^{\circ} \)

Description for Correct answer:

\( \Large \angle AOB \ becomes\ a\ straight\ line\ if\ \angle AOB = 180 ^{\circ} \)

Now, \( \Large \angle AOB = \angle BOC + \angle COA \)

Therefore, \( \Large 180 ^{\circ} = 7x ^{\circ} + 20 ^{\circ} + 3x ^{\circ} \)

=> \( \Large 10x ^{\circ} = 160 ^{\circ} \)

=< \( \Large x ^{\circ} = \frac{160}{10} = 16 ^{\circ} \)

Part of solved Loci and concurrency questions and answers : >> Elementary Mathematics >> Loci and concurrency

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