Ex.3.3 Q12 Understanding Quadrilaterals Solution-Ncert Maths Class 8

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Find the measure of \(\angle {\rm{P }}\) and \(\angle {\rm{S}}\) if \(SP\) is parallel to \(RQ\) in Fig .

(If you find \({\rm{m}}\angle {\rm{R}}\), is there more than one method to find \({\rm{m}}\angle {\rm{P}}\,?\)

 Video Solution
Understanding Quadrilaterals
Ex 3.3 | Question 12

Text Solution

What is Known?

Given figure is a Quadrilateral.

What is Unknown?

Find \({\rm{m}}\angle P\,{\rm{ and}\, {m}}\angle S\)


Sum of the measures of all the interior angles of a quadrilateral is \(360^\circ\).


Given \(SP\) is parallel \(RQ\) and \(SR\) is the traversal drawn to these lines. Hence,

\[\begin{align}\angle \text{S}+\angle \text{R}&={{180}^{\text{o}}}\\\angle \text{S}+{{90}^{\circ}}&={{180}^{\circ}}  \\\angle \text{S}&={{180}^{\circ}}-{{90}^{\circ}}  \\\angle \text{S}&={{90}^{\circ}}  \\

Using the angle sum property of a quadrilateral,

\[\begin{align}\angle \text{S}+\angle \text{P}+\angle \text{Q}+\angle \text{R}&={{360}^{\text{o}}} \\{{90}^{\text{o}}}+\angle \text{P}+{{130}^{\text{o}}}+{{90}^{\text{o}}}&={{360}^{\text{o}}} \\\angle \text{P}+{{310}^{\text{o}}}&={{360}^{\text{o}}} \\\angle \text{P}&\!\!=\!{{360}^{\text{o}}}\!\!-\!\!{{310}^{\text{o}}} \\\angle \text{P}&={{50}^{\text{o}}} \\\end{align}\]