Mathematics

# In the figure,$\Delta PQR$ is a right angled at Q, $\overline {ML} ||\overline {RQ}$ and $\angle LMR = {130^ \circ }$. Find $\angle LPM$ and $\angle PML$

##### SOLUTION

Given: $\angle Q = {90^0}$

$ML\parallel RQ$

$\angle LMR = {130^0}$

To find: $\angle LPM = ?$

$\angle PML = ?$

Statement

1. $\angle PML + \angle LMR = {180^0}$

$\Rightarrow \angle PML + {130^0} = {180^0}$

$\Rightarrow \angle PML = {50^0}$

2. $\angle PLM = \angle PQR$

$= {90^0}$

3. $\angle PLM + \angle PML + \angle LPM = {180^0}$

$\Rightarrow {90^0} + {50^0} + \angle LPM = {180^0}$

$\Rightarrow \angle LPM + {140^0} = {180^0}$

$\Rightarrow \angle LPM = {40^0}$

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Subjective Medium Published on 09th 09, 2020
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