What is \[2\angle APB\] equivalent to?
A) \[\angle A+\angle B\]
B) \[\angle A+\angle C\]
C) \[\angle B+\angle D\]
D) \[\angle A-\angle D\]
Correct Answer: A
Solution :
\[\angle 2+\angle 3+\angle APB={{180}^{o}}\] \[\Rightarrow \]\[\angle 1+\angle 4+\angle APB={{180}^{o}}\] (Since \[\angle 2=\angle 1\]and\[\angle 3=\angle 4.\]) \[\Rightarrow \]\[2\angle 1+2\angle 3+2\angle APB={{360}^{o}}\] \[\Rightarrow \]\[\angle APB=\angle A+\angle B\]
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