Question

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

• A.

  ${315}^{\circ }$

• B.

  ${105}^{\circ }$

• C.

  ${210}^{\circ }$

• D.

  ${270}^{\circ }$

Answer 1

The correct option is C

${210}^{\circ }$

Given, $\angle$x = ${75}^{\circ }$ Hence, $\angle$z = ${75}^{\circ }$ (vertically opposite angles) $\angle$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 = ${210}^{\circ }$