Gujarat BoardEnglish MediumSTD 8MATHSUnderstanding Shapes – II (Quadrilaterals)3 Marks
Question
In the figure, find the measure of $\angle\text{MPN}$.
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Answer
In the figure, $OMPN$ is a quadrilateral in which $\angle\text{O}=45^\circ$
$\angle\text{M}=\angle\text{N}=90^\circ$
$(PM \perp OA$ and $PN \perp OB)$
Let, $\angle\text{MPN}=\text{x}^\circ$
$\angle\text{O}+\angle\text{M}+\angle\text{N}+\angle\text{MPN}$
$=360^\circ$ (Sum of angles of a quadrilateral)
$\Rightarrow45^\circ+90^\circ+90^\circ+\text{x}^\circ$
$=360^\circ$
$\Rightarrow225^\circ+\text{x}^\circ$
$=360^\circ$
$\Rightarrow\text{x}^\circ=360^\circ-225^\circ$
$\Rightarrow\text{x}^\circ=135^\circ$
$\angle\text{MPN}=135^\circ$
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