Question

The value of x in the given figure is-

${\text{A}}{\text{. 2}}{0^ \circ }$
${\text{B}}{\text{. 22}}{{\text{3}}^ \circ }$
${\text{C}}{\text{. 11}}{{\text{8}}^ \circ }$
${\text{D}}{\text{. 7}}{{\text{2}}^ \circ }$

Answer 1

Hint: Refer the figure below to find x. From the figure we can say, x + y = 360 (whole angle).

Complete Step-by-Step solution:
Using the figure in Hint:
We know $x + y = {360^ \circ }$ (whole angle)
$x = {360^ \circ } - y \to (1)$
Now, ${48^ \circ } + {30^ \circ } + {40^ \circ } + y = {360^ \circ }$ (forming a quadrilateral)
$
  {48^ \circ } + {30^ \circ } + {40^ \circ } + y = {360^ \circ } \\
   \Rightarrow y = {360^ \circ } - ({118^ \circ }) \\
  \therefore y = {242^ \circ } \\
$
Putting the value of y in equation (1)-
$
  x = {360^ \circ } - {242^ \circ } \\
  x = {118^ \circ } \\
 $
Hence, the value of x is 118 degrees.
Therefore, the correct option is ${\text{C}}{\text{. 11}}{{\text{8}}^ \circ }$.

Note: Whenever such types of questions appear then assume an angle y in the given figure such that x + y = 360 degrees and name it as equation 1 and then put the sum of the angles of quadrilateral ABYC equal to 360 degrees then from here find the value of y, put this in equation 1 to find x.