Question

In the figure(not drawn to scale), $ABCD$ is a rhombus and $CGEF$ is a square. Find $y$.

• A. ${30}^o$
• B. ${50}^o$
• C. ${60}^o$
• D. ${70}^o$

Answer 1

Answer: (C)

${60}^o$

We know that all sides of rhombus are equal

in triangle $ADC$, w have

$CD=AD$ .... sides of rhombus

$\Rightarrow \angle DCA=\angle CAD=x$

$\Rightarrow x+x+{120}^{\circ }={180}^{\circ }$

$\Rightarrow x={30}^{\circ }$

$CGEF$ is a square and each angle is of ${90}^{\circ }$.

Thus $\angle CGF=x+y={90}^{\circ }$

$\Rightarrow y+{30}^{\circ }={180}^{\circ }$

$\Rightarrow y={60}^{\circ }$