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Question

The theorem says that "The measure of an exterior angle of a triangle is sum of the interior opposite angles". Select the correct option from the followings


A
POQ=2PAQ
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B
POQ=2PAB
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C
POQ=2QAB
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D
POQ=PAQ
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Solution

The correct option is A POQ=2PAQ
According to the theorem,
POB=PAO+APO
Similarily,
QOB=QAO+AQO
Now,
PAO=APO,
POB=2PAO
QAO=AQO,
QOB=2QAO
(as same sides have similar angles)
And
POQ=POB+QOB
PAQ=PAO+QAO
So,
POQ=POB+QOB
=2PAO+2QAO
=2(PAO+QAO)
=2PAQ






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