Please solve q 21?

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1 Answer
CW
May 12, 2018

#k=1/2#

Explanation:

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As consecutive angles of a parallelogram are supplementary,
#=> angleP+angleQ=180^@#
#=> 3x+3y=180^@, => 3(x+y)=180^@, => x+y=60^@#
In #DeltaPNQ, anglePNQ=180-(x+y)=180-60=120^@#
In #DeltaPMQ, anglePMQ=180-2(x+y)=180-(2*60)=60^@#
given that #k*anglePNQ=anglePMQ#,
#=> k=(anglePMQ)/(anglePNQ)=60/120=1/2#

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