Question

In the below Fig. $OA\text{and}OB$ are opposite rays:
$\left(i\right)$ if $x={25}^{\circ },$ what is the value of $y?$

Answer 1

Given: $x={25}^{\circ }$

From the given figure,

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

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

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

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

$2y+5^{\circ }+3\left({25}^{\circ }\right)={180}^{\circ }$

$2y+{80}^{\circ }={180}^{\circ }$

$2y={180}^{\circ }-{80}^{\circ }$

$2y={100}^{\circ }$

$y={50}^{\circ }$

Hence, the value of $y={50}^{\circ }.$