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Question 155
In parallelogram MODE, the bisectors of M and O meet at Q. Find the measure of MQO


Solution

Let MODE be a parallelogram and Q be the point of intersection of the bisector of M and O

Since, MODE is a parallelogram,
EMO+DOM=180    [ adjacent angles are supplementary]
12EMO+12DOM=90      [dividing both sides by 2]
QMO+QOM=90      ........ (i)
Now, in ΔMOQ,
QOM+QMO+MQO=180    [angle sum property of triangle]
90+MQO=180     [from Eq. (i)]
MQO=18090=90

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