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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