Question

In parallelogram MODE, the bisector of ∠M and ∠O meet at Q, find the measure of ∠MQO.

Answer 1

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°