Question

in the figure triangle PQR is a right angled at Q, ML is parallel to RQ and angle LMR is equal to 130 degree. find angle LPM angle PML and angle PRQ

Answer 1

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Answer 2

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.