Solved Examples

1. In the adjoining figure, find ∠$\mathrm{\angle }$ C. If AB // CD

Sol:   ∠$\mathrm{\angle }$ E = 180 - 120 = 60

∠$\mathrm{\angle }$ E + ∠$\mathrm{\angle }$ X + ∠$\mathrm{\angle }$ F = 180 ⇒$\Rightarrow$ 60 + 50 + F = 180 ⇒$\Rightarrow$ F = 70
Now ∠$\mathrm{\angle }$ G = 180 - F = 110.
As AB // CD, ∠$\mathrm{\angle }$G = ∠$\mathrm{\angle }$C
So ∠$\mathrm{\angle }$C = 110

2. Find the value of x in following figure.

Sol: As C // E, ∠$\mathrm{\angle }$B = ∠$\mathrm{\angle }$Y

Also ∠$\mathrm{\angle }$Y + ∠$\mathrm{\angle }$Z = 180 ⇒$\Rightarrow$  ∠$\mathrm{\angle }$Z = 180 - 130 = 50

Now in Δ$\mathrm{\Delta }$ AGF, ∠$\mathrm{\angle }$A + ∠$\mathrm{\angle }$Z + ∠$\mathrm{\angle }$X = 180  ⇒$\Rightarrow$ ∠$\mathrm{\angle }$X = 180 - 20 - 50 = 110

3. Find ∠$\mathrm{\angle }$OBD in the given figure. It is given that EC || AO.

Sol:   From the diagram, in Δ$\mathrm{\Delta }$OBD, 110 + 20 + ∠$\mathrm{\angle }$B = 180 ⇒$\Rightarrow$ ∠$\mathrm{\angle }$B = 50

4. If the two lines n and m are parallel, then find the value of ϕ$\varphi$ in the given figure.

Sol:  Draw a parellel to n. Now from the diagram ϕ$\varphi$ = 50 + 30 = 80 (Alternate interior angles are equal)

Alternate method:  you can also solve this problem by calculating interior angles of the triangle.