Question

In the figure, two lines intersect at O. If x = ${75}^{\circ }$, find $\angle u$ + $\angle y.$

Answer 1

Given, $\angle x={75}^{\circ }$

$\angle x+\angle y={180}^{\circ }$ (by linear pair)

${75}^{\circ }+\angle y={180}^{\circ }$

$\angle y={180}^{\circ }–{75}^{\circ }$

i.e, $\angle y={105}^{\circ }$
Now,
$\angle y=\angle u$ (vertically opposite angles)

Therefore, $\angle u={105}^{\circ }$
Hence, $\angle u+\angle y={210}^{\circ }$