In Fig., line l∥m and a transversal n cuts them at P and Q respectively. If ∠1=75∘, find all other angles.
In the given figure, l∥m , n is a transversal line and ∠1=75∘
Thus, we have:
∠1+∠2=180∘ [Since, Linear pair]
⇒∠2=180∘−∠1
⇒∠2=180∘−75∘
⇒∠2=105∘
Now, ∠1=∠3=75∘ [Vertically opposite angles]
∠1=∠5=75∘ [Corresponding angles]
∠5=∠7=75∘ [Vertically opposite angles]
∠2=∠6=105∘ [Corresponding angles]
∠8=∠6=105∘ [Vertically opposite angles]
∠4=∠2=105∘ [Vertically opposite angles]
Therefore,
∠2=105∘
∠3=75∘
∠4=105∘
∠5=75∘
∠6=105∘
∠7=75∘
∠8=105∘