Question

In the given figure $BC=AC=AD$ and $\angle EAD={81}^{\circ }$ Find the value of $x$

• A. ${45}^{\circ }$
• B. ${54}^{\circ }$
• C. ${63}^{\circ }$
• D. ${36}^{\circ }$

Answer 1

The correct option is B ${54}^{\circ }$

Consider the diagram shown below.

Here, we have four equations.

$2a+c={180}^{\circ }$ ...... (1)

$x+c={180}^{\circ }$ ...... (2)

$2x+b={180}^{\circ }$ ...... (3)

$a+b+{81}^{\circ }={180}^{\circ }$

$a+b={99}^{\circ }$ ...... (4)

Multiply $2$ to equation (4) and add it to the equation (2).

$2a+2b+x+c={378}^{\circ }$

Substitute equation (1) in the above result.

${180}^{\circ }+2b+x={378}^{\circ }$

$2b+x={198}^{\circ }$ ...... (5)

From equations (3) and (5), we have

$3x={162}^{\circ }$

$x={54}^{\circ }$

Hence, the value of $x$ is ${54}^{\circ }$.