Question

In the adjoining figure, Find the unknown angles.

Answer 1

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

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