Question

Use the information given in figure to choose the correct value of $x$.

• A. $x={86}^o$
• B. $x={60}^o$
• C. $x={68}^o$
• D. $x={107}^o$

Answer 1

Answer: (C)

$x={68}^o$

Since, $EAB$ is a straight line
$\therefore \angle DAE+\angle DAB={180}^{\circ }$ ....[Linear pair]
$\Rightarrow {73}^{\circ }+\angle DAB={180}^{\circ }$.

Since, by angle sum property, the sum of the angles of quadrilateral $ABCD$ is ${360}^o$.
$\angle ADC+\angle DCB+\angle CBA+\angle BAD={360}^o$
$\therefore {107}^{\circ }+{105}^{\circ }+x+{80}^{\circ }={360}^{\circ }$
$\Rightarrow {292}^{\circ }+x={360}^{\circ }$

$x={360}^{\circ }-{292}^{\circ }={68}^{\circ }$.

Therefore, option $C$ is correct.