Question

In the figure,∆PQR is right angled at Q,ML||RQ and LMR=130°.Find angle LPM,PML and PRQ.

Answer 1

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Answer 2

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Answer:

The measure of angle LPM is 40 degree. The measure of PML is 50 degree. The measure of PRQ is 50 degree.

Step-by-step explanation:

Given information: Triangle PQR is a right angled triangle, ∠Q=90°.

\angle LMR=130^{\circ}

Angle PML and angle LMR are supplementary angles, because they are lie on a straight line.

\angle LMR+\angle PML=180^{\circ}

130^{\circ}+\angle PML=180^{\circ}

\angle PML=50^{\circ}

Therefore the measure of PML is 50 degree.

Angle PML and angle PRQ are corresponding angles and corresponding angles are equal.

\angle PRQ=\angle PML

\angle PRQ=50^{\circ}

Therefore the measure of PRQ is 50 degree.

According to the angle sum property the sum of interior angles of a triangle is 180 degree.

Use angle sum property is triangle PQR,

\angle LPM+\angle PQR+\angle PRQ=180^{\circ}

\angle LPM+90^{\circ}+50^{\circ}=180^{\circ}

\angle LPM=40^{\circ}

Therefore the measure of angle LPM is 40 degree.

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