Gujarat BoardEnglish MediumSTD 8MATHSUnderstanding Quadrilaterals and Practical Geometry2 Marks
Question
Find the value of $x$ in the trapezium $ABCD$ given below.
✓
Answer
Given, a trapezium $ABCD$ in which $\angle=(\text{x}-20)^\circ,\angle\text{D}=(\text{x}+40)^\circ$
Since, in a trapezium, the angles on either side of the base are supplementary, therefore
$(\text{x}-20)+(\text{x}+40)=180^\circ$
$\Rightarrow\text{x}-20+40=180^\circ$
$\Rightarrow\text{2x}=20=180^\circ$
$\Rightarrow\text{2x}=(180^\circ+20^\circ)=160^\circ$
$\Rightarrow\text{x}=80^\circ.$
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