Question

In the given figure OA and OB are opposite rays:

i) If x = 75${}^{\circ }$, then what is the value of y?

ii) If y = 110${}^{\circ }$, then what is the value of x?

Answer 1

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

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

⇒ x + y =180${}^{\circ }$ ........ (a)

i) If x = 75${}^{\circ }$, then from (a)

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

⇒ y = 105${}^{\circ }$

ii) If y = 110 then from (a)

⇒ x + 110${}^{\circ }$ = 180${}^{\circ }$

⇒ x = 70${}^{\circ }$