A) \[\angle C+\angle D\]
B) \[\angle A+\angle C\]
C) \[\angle B+\angle D\]
D) \[2\angle C\]
Correct Answer: A
Solution :
(a)\[\angle A+\angle B+\angle C+\angle D={{360}^{{}^\circ }}\] \[\frac{\angle A}{2}\text{+}\frac{\angle B}{2}\text{+}\frac{\angle C}{2}\text{+}\frac{\angle D}{2}={{180}^{{}^\circ }}~~\] \[{{180}^{{}^\circ }}-\angle APB+\frac{\angle C}{2}+\frac{\angle D}{2}={{180}^{{}^\circ }}\] \[\Rightarrow \]\[\angle APB=\frac{\angle C}{2}+\frac{\angle D}{2}\] \[2\angle APB=\angle C+\angle D.\]You need to login to perform this action.
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