Question

In the below Fig. $OA\text{and}OB$ are opposite rays:
$\left(ii\right)$ If $y={35}^{\circ },$ what is the value of $x?$

Answer 1

Given: $y={35}^{\circ }$

From the given figure,

$\angle AOC=(2y+5{)}^{\circ }$ and $\angle BOC=3x^{\circ }$

Since, $\angle AOC$ and $\angle BOC$ form a linear pair

$\therefore \angle AOC+\angle BOC={180}^{\circ }$

$(2y+5{)}^{\circ }+3x^{\circ }={180}^{\circ }$

$2\left({35}^{\circ }\right)+5^{\circ }+3x^{\circ }={180}^{\circ }$

$3x^{\circ }+{75}^{\circ }={180}^{\circ }$

$3x^{\circ }={180}^{\circ }-{75}^{\circ }$

$3x^{\circ }={105}^{\circ }$

$x^{\circ }={35}^{\circ }$

Hence, the value of $x^{\circ }={35}^{\circ }.$