Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

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 = ${210}^{\circ }$