Question

From the following figure find ,
(i) x
(ii) $\angle ABC$
(iii) $\angle ACD$

Answer 1

In a quadrilateral $ABCD$

$i)$ Sum of all angles is ${360}^{\circ }$

$\Rightarrow \angle A+\angle B+\angle C+\angle D={360}^{\circ }$

$\Rightarrow {48}^{\circ }+x+4x+3x+4x={360}^{\circ }$

$\Rightarrow 12x={312}^{\circ }$

$\Rightarrow x={26}^{\circ }$

$ii)\angle ABC=4x=4\times {26}^{\circ }={104}^{\circ }$

$iii)$ In $△ACD$

$\Rightarrow \angle ADC+\angle CAD+\angle ACD={180}^{\circ }$

$\Rightarrow \angle ACD+4x+{48}^{\circ }={180}^{\circ }$

$\Rightarrow \angle ACD={180}^{\circ }-{48}^{\circ }-{104}^{\circ }={28}^{\circ }$