Question

In triangle PQR, a line segment is drawn, which intersects the sides PQ and PR at M and N respectively. If MN|QR, PMN = 75°, and PRQ = 40°, find the measurements of PQR and QPR. ​

Answer 1

Answer:

∠PQR = 75°,  ∠QPR = 65°

Step-by-step explanation:

Refer to the image.

As MN|QR,

∠PMN = ∠PQR (Alternate interior angles)(PQ is the transversal)

and

∠PRQ = ∠PNM(Alternate interior angles)(PR is the transversal)

Thus, ∠PQR = 75° and ∠PNM = 40°

Now, in ΔPQR

Sum of all interior angles = 180°

So,

∠PMN + ∠PNM + ∠QPR = 180°

75° + 40° + ∠QPR = 180°

∠QPR = 180° - (75°+40°)

∠QPR = 180° - 115°

Thus, ∠QPR = 65°

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Answer 2

Answer:

Angle PMN = Angle PQR ( alternate interior angles)

Angle PQR °= 75°

let the angle be = x

75°+40°+x = 180°

115°+x =180°

x = 180°-115°

x = 65° answer