Question

Question 88

A road crosses a railway line at an angle of ${30}^{\circ }$ as shown in the figure. Find the values of a, b and c.

Answer 1

Lines l and m are parallel, P is transversal and $x={30}^{\circ }$
Therefore
$\Rightarrow y={30}^{\circ }\text{Now},c+y={180}^{\circ }\left[\text{linear pair}\right]$
$\Rightarrow c+{30}^{\circ }={180}^{\circ }\Rightarrow c=180-{30}^{\circ }\Rightarrow c={150}^{\circ }$
Now, $\angle 1+c={180}^{\circ }\left[\text{linear pair}\right]\Rightarrow \angle 1+{150}^{\circ }={180}^{\circ }\Rightarrow \angle 1={180}^{\circ }-{150}^{\circ }\therefore \angle 1=a\left[\text{corresponding angles}\right]\Rightarrow a={30}^{\circ }$
Also, $\angle 2+a={180}^{\circ }\left[\text{linear pair}\right]\Rightarrow \angle 2+{30}^{\circ }={180}^{\circ }\Rightarrow \angle 2={180}^{\circ }-{30}^{\circ }={150}^{\circ }$
Again,$\angle 2=b\left[\text{alternate interior angles}\right]\Rightarrow b={150}^{\circ }$
Hence, $a={30}^{\circ },b={150}^{\circ }\text{and}c={150}^{\circ }$.