Question

$ABCD$ is a square and $BCE$ is an equilateral triangle. Find the value of $a,b$ and reflex $\angle BED$

• A. ${20}^o,{70}^o,{230}^o$
• B. ${18}^o,{72}^o,{210}^o$
• C. ${15}^o,{75}^o,{225}^o$
• D. ${25}^o,{65}^o,{210}^o$

Answer 1

The correct option is C ${15}^o,{75}^o,{225}^o$

$ABCD$ is a square and $BCE$ is an equilateral triangle

$\angle CEB=\angle EBC=\angle ECB={60}^0$

Since $ABCD$ is a square,

$\angle DCB={90}^0$

Now $\angle DCB=\angle DCE+\angle ECB$

$\Rightarrow {90}^0=\angle DCB+{60}^0$

$\Rightarrow \angle DCE={30}^0$

Now in triangle $DCE$,,

$EC=DC$

$\therefore \angle CDE=\angle DEC=x$ (let)

Again, $\angle EDC+\angle DEC+\angle DCE={180}^0$

$\Rightarrow x+x+360=180$

$\Rightarrow 2x=150$

$\Rightarrow x=7560$

$\therefore b={75}^0$

Now, $\angle ADC={90}^0$

$\Rightarrow \angle ADE+\angle EDC={90}^0$

$\Rightarrow a+{75}^0={90}^0$

$\Rightarrow a={15}^0$

Now, reflex $\angle BED=36060-\angle BED$

$\Rightarrow {360}^0-(\angle DEC+\angle BEC)$

$\Rightarrow {360}^0-({75}^0-{60}^0)$

$\Rightarrow {360}^0-13560$

$\Rightarrow {225}^0$