Question

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

Answer 1

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Answer 2

Solution :

In ∆PQR is right angled at Q ,

ML//RQ and <LMR = 130°

i ) ML // RQ , PR is a transversal,

<PRQ + <LMR = 180°

[ Sum of interior angles same side

of the transversal are supplementary ]

<PRQ + 130° = 180°

=> <PRQ = 180° - 130°= 50° ----( 1 )

ii ) <LMR + <PML = 180°

[ Linear pair ]

=> 130° + <PML = 180°

=> <PML = 180° - 130° = 50° ----( 2 )

iii ) In ∆PQR ,

<PRQ + <PQR + <QPR = 180°

=> 50° + 90° + <LPM = 180°

=> 140° + <LPM = 180°

=> <LPM = 180° - 140°

=> <LPM = 40°

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