Question

In the given figure OA and OB are opposite rays:

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

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Answer 1

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

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

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

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

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

⇒ y = 105${}^{\circ }$