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Question
In parallelogram MODE, the bisector of ∠M and ∠O meet at Q, find the measure of ∠MQO.
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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]
⇒ `1/2` ∠EMO + `1/2` ∠DOM = 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 equation (i)]
∴ ∠MQO = 180° – 90° = 90°
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