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 \(x\).

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)

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

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

In parallelogram \(CLUE\)

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

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

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