Question

in triangle pqr pq/pr=qm/mr ∠q=75 and ∠r=45 find the measure of ∠ qpm

Answer 1

Answer:

Question ⤵

In triangle pqr pq/pr=qm/mr ∠q=75 and ∠r=45 find the measure of ∠ qpm .

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Let's assume angle Q =75° =angle 1

and angle R =45° = angle 2

angle P (angle QPM) = angle 3

Therefore,

By angle sum property,

Angle 1 +angle 2 + angle 3 = 180°

75°+ 45° + angle 3 = 180°

120°+angle 3 = 180°

Angle 3 = 180° -120° = 60°

Angle PQM = 60°

Thanks...

Answer 2

Solution :-

In ∆PQR we have,

→ ∠PQR = 75°

→ ∠PRQ = 45°

So,

→ ∠PQR + ∠PRQ + ∠QPR = 180° { By angle sum property. }

→ 75° + 45° + ∠QPR = 180°

→ 120° + ∠QPR = 180°

→ ∠QPR = 180° - 120°

→ ∠QPR = 60°

Also given that, In ∆PQR,

→ PQ/PR = QM/MR

Therefore , we can conclude that, PM is angle bisector of ∠QPR .

hence,

→ ∠QPM = (1/2)•∠QPR

→ ∠QPM = (1/2) * 60°

→ ∠QPM = 30° (Ans.)

∴ the measure of ∠QPM is equal to 30° .

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