Question

In the given figure, sides AB and CD of the quadrilateral ABCD are produced. Find the value of \(x\).

• A. ${75}^{\circ }$
• B. ${80}^{\circ }$
• C. ${70}^{\circ }$
• D. ${65}^{\circ }$

Answer 1

The correct option is B

${80}^{\circ }$

Since, $\angle ADE+\angle ADC={180}^{\circ }$ [Linear pair]
$\Rightarrow {100}^{\circ }+\angle ADC=180[\because \angle ADE={100}^{\circ }]$
$\Rightarrow \angle ADC={180}^{\circ }-{100}^{\circ }={80}^{\circ }$
In quadrilateral ABCD
$\angle ADC+\angle A+\angle ABC+\angle C={360}^{\circ }$
$\because$ [Sum of all angles of a quadrilateral is ${360}^{\circ }$]
$\Rightarrow {80}^{\circ }+{60}^{\circ }+\angle ABC+{120}^{\circ }={360}^{\circ }$
$\Rightarrow \angle ABC+{260}^{\circ }={360}^{\circ }$

$\Rightarrow \angle ABC={100}^{\circ }$
But, $\angle ABC+x={180}^{\circ }$ [Linear pair]
$\therefore {100}^{\circ }+x={180}^{\circ }$
Hence, $x={80}^{\circ }$