Question

The bisectors of ∠ P and ∠Q intersect in point M for †PQRS. If ∠R = 700 and ∠S = 500 . Determine ∠ PMQ​

Answer 1

Answer: ∠PMQ = 60°

Step-by-step explanation:

∠ P + ∠ Q + ∠ R + ∠ S = 360

∠ P + ∠ Q + 70 + 50 = 360

∠ P + ∠ Q = 240 --------------------- (1)

The bisectors of ∠ P and ∠Q intersect in point M,

therefore, ∠P = 2∠MPQ -----------------(2)

                ∠Q = 2 ∠MQP ------------------(3)

From (1) ,(2) and (3)

2∠MPQ + 2∠MQP = 240

2(∠MPQ + ∠MQP) = 240

∠MPQ + ∠MQP = 120

Now in ΔPMQ,

∠MPQ + ∠MQP + ∠PMQ = 180 (Angle sum property)

120 + ∠PMQ = 180

∠PMQ = 180 - 120

∠PMQ = 60°

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