Question

In the given figure, ABCS is a rhombus. Find x.

• A. ${39}^0$
• B. ${40}^0$
• C. ${49}^0$
• D. ${29}^0$

Answer 1

The correct option is A ${39}^0$

Since, ABCD is a rhombus.

$\angle ABC=\angle ADC={100}^{\circ }$ (Opposite angles of a rhombus are equal)

In $△ABC$

$A=BC$

So, $\angle BCA=\frac{1}{2}({180}^{\circ }-{100}^{\circ })={40}^{\circ }$

In $△EAC$

$\angle ECA={180}^{\circ }-{33}^{\circ }+{68}^{\circ }$

$={180}^{\circ }-{101}^{\circ }={79}^{\circ }$

Now,

$\angle ECA=\angle BCA+x$

$\Rightarrow {79}^{\circ }={40}^{\circ }+x$

$\Rightarrow x={39}^{\circ }$

Hence, A is the correct option.