Q3 Pls Solve it fast Its Urgent
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Answers
Or maybe 85 degree
PQ and RS are parallel.
Hope it helps uuu
This is so simple!
We know that, for any quadrilateral, the sum of all interior angles is 360°.
In quadrilateral PQRS, the sum of interior angles is 360°.
∠PQR + ∠QRS + ∠RSP + ∠SPQ = 360°
Given that ∠RSP = 60° & ∠QRS = 110°.
∴ ∠SPQ + ∠PQR = 360 - (∠RSP + ∠QRS)
= 360 - (60 + 110)
= 360 - 170 = 190°
∴∠SPQ + ∠PQR = 190°
PM & QM are bisectors.
∴ ∠MPQ = ∠SPQ / 2
& ∠MQP = ∠PQR / 2
Consider ΔPQM.
∠MPQ + ∠MQP
= (∠SPQ / 2) + (∠PQR / 2)
= (∠SPQ + ∠PQR) / 2
= 190° / 2
= 95°
∴ ∠MPQ + ∠MQP = 95°
For any triangle, the sum of all interior angles is 180°.
∠MPQ + ∠MQP + ∠PMQ = 180°
∴ ∠PMQ = 180 - (∠MPQ + ∠MQP)
= 180 - 95
= 85°
∴ ∠PMQ = 85°
In the fig., the three quadrilaterals are the chances to have been that as in the question.
In the first quadrilateral, ∠SPQ and ∠PQR are obtuse and acute respectively.
In the third quadrilateral, ∠SPQ and ∠PQR are acute and obtuse respectively.
The feature of the second quadrilateral is, PQ is parallel to RS.
PM and QM of each quadrilaterals are angle bisectors. As the angles SPQ and PQR change, ∠PMQ is always 85°, doesn't change.
Here is the simple method for calculating ∠PMQ:- add angles RSP and QRS and then divide it by 2. That's all!
(∠RSP + ∠QRS) / 2 = (60° + 110°) / 2 = 170° / 2 = 85°
Hope this may be helpful.
Please mark my answer as the brainliest if this may be helpful.
Thank you. Have a nice day.
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