Question
In parallelogram MODE, the bisectors of ∠M and ∠O meet at Q. Find the measure of ∠MQO
In parallelogram MODE, the bisectors of ∠M and ∠O meet at Q. Find the measure of ∠MQO
Answer:
:
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]
12∠EMO+12∠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 Eq. (i)]
∴∠MQO=180∘−90∘=90∘
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:
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]
12∠EMO+12∠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 Eq. (i)]
∴∠MQO=180∘−90∘=90∘
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