Ex.3.3 Q11 Understanding Quadrilaterals Solution-Ncert Maths Class 8

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Question

 Find \({\rm{m}}\,\angle {\rm{C }}\) in Fig \(3.33\) if \(AB \) is parallel to \( DC\).

Text Solution

What is Known?

Given figure is a Quadrilateral with two sides running parallel and one angle is given.

What is Unknown?

Find \({\rm{m }}\angle {\rm{C}}\)

Reasoning:

Trapezium is a quadrilateral with one pair of parallel sides.

Steps:

Given figure \(ABCD\) is a Trapezium, in which \(AB\) is parallel to \( DC\).

Here,

\[\begin{align}\angle {\rm{B}} + {\rm{ }}\angle {\rm{C }} &= {\rm{18}}0^\circ \left[ {{\text{pair of adjacent angles are supplementary}}} \right]\\{\rm{12}}0^\circ + {\rm{ }}\angle {\rm{C}} &= {\rm{18}}0^\circ \\
\angle {\rm{C }} &= {\rm{18}}0^\circ {\rm{ }} - {\rm{12}}0^\circ \\\angle {\rm{C }} &= {\rm{ 6}}0^\circ \\
{\rm{Therefore \,m}}\,\angle {\rm{C }} &= {\rm{6}}0^\circ\end{align}\]