Question

In the given figure, the two lines AB and CD intersect at a point O such that $\angle BOC={125}^{\circ }$. Find the values of x,y and z.

Answer 1

Here, ∠AOC and ∠BOC form a linear pair.

∴ ∠AOC + ∠BOC = 180${}^o$

⇒ x${}^o$ + 125${}^o$ = 180${}^o$

⇒ x${}^o$ = 180${}^o$ − 125${}^o$​ = 55${}^o$

Now,

∠AOD = ∠BOC = 125${}^o$

(Vertically opposite angles)

∴ y${}^o$= 125${}^o$

∠BOD = ∠AOC = 55${}^o$

(Vertically opposite angles)

∴ z${}^o$ = 55${}^o$

Thus, the respective values of x, y and z are 55${}^o$, 125${}^o$ and 55${}^o$.