Solveeit Logo
Login

Question

Mathematics Question on Checking For Parallel Lines

In the adjoining figure, Find the unknown angles.
adjoining figure of lines and angles

Answer

Given, p∣∣qp||q and cut by a transversal line.
∵\because 125∘+e=180∘125\degree+e=180\degree [Linear pair]
∴  e=180∘−125∘=55∘\therefore \;e=180\degree-125\degree=55\degree ……….(i)
Now ee = =f=55∘=f=55\degree [Vertically opposite angles]
Also a=f=55∘a=f=55\degree [Alternate interior angles]
a+b=180∘a+b=180\degree[Linear pair]
⇒55∘+b=180∘\Rightarrow 55\degree+b=180\degree [From eq. (i)]
⇒b=180∘−55∘=125∘\Rightarrow b=180\degree-55\degree=125\degree
Now a=c=55∘a=c=55\degree and b=d=125∘b=d=125\degree [Vertically opposite angles]

Thus, a=55∘,b=15∘,c=55∘,d=125∘,e=55∘a=55\degree,b=15\degree,c=55\degree,d=125\degree,e=55\degree and f=55∘f=55\degree