Ex.3.3 Q9 Understanding Quadrilaterals Solution-Ncert Maths Class 8

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Question

In the above figure both \(RISK\) and \( CLUE\) are parallelograms. Find the value of \(x\).

 Video Solution
Understanding Quadrilaterals
Ex 3.3 | Question 9

Text Solution

What is Known?

In the given figure \(RISK \)and \(CLUE\) are parallelograms.

What is Unknown?

Values of \(x\)

Reasoning:

The diagonals of a parallelogram bisect each other. Also, in a parallelogram, opposite angles are equal and adjacent angles are supplementary. Using this property, we can calculate the unknown angles.

Steps:

In parallelogram \(RISK\)

\({\rm{RKS }} + \angle {\rm{ISK }} = {\rm{ 18}}0^\circ \)  (Adjacent angles of a parallelogram are supplementary)

\[\begin{align}{\rm{12}}0^\circ + \,\angle {\rm{ISK }} &= {\rm{18}}0^\circ \\\angle {\rm{ISK }} &= {\rm{ 6}}0^\circ\end{align}\]

\[\begin{align}{\angle {\text{I}}}&{ = \angle {\rm{K}}}\,{\left( \begin{array}{l}{\text{In parallelogram opposite }}\\{\text{angles are equal}}\end{array} \right)}\\&{ = {\rm{12}}{0^\circ }}&\end{align}\]

In parallelogram \(CLUE\)

\[\begin{align}{\angle {\rm{L}}}&{ = \angle {\rm{E}}}\,{\left( \begin{array}{l}{\text{In parallelogram opposite}}\\{\text{ angles are equal}}\end{array} \right)}\\&{ = {\rm{7}}{0^\circ }}&\end{align}\]

The sum of the measures of all the interior angles of a triangle is \(180^\circ.\)

\[\begin{align}x+{{60}^{\circ}}+{{70}^{\circ}}&={{180}^{\circ}} \\x+130&={{180}^{\circ}}  \\x&={{180}^{\circ}}-{{130}^{\circ}}  \\x&={{50}^{\circ}}  \\\end{align}\]