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 \( DC\).

 Video Solution
Understanding Quadrilaterals
Ex 3.3 | Question 11

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,

\[\begin{align}\angle {\rm{B}} + \angle {\rm{C}} &= {180^ \circ }\left[ \begin{array}{l}{\text{pair of adjacent }}\\{\text{angles are }}\\{\text{supplementary}}\end{array} \right]\\{\rm{12}}{0^\circ } + \angle {\rm{C}} &= {180^ \circ }\\\angle {\rm{C}} &= {180^ \circ }\\\angle {\rm{C}} &= {180^ \circ } - {120^ \circ }\\\angle {\rm{C  }}&={60^ \circ }\\\therefore \,\,m\angle {\rm{C }}&={60^ \circ }\end{align}\]