In the following figure, if l || m, then find the measures of angles marked by a and b.

a = 70° and b = 110°

Concept used

For two parallel lines,

Corresponding angles are equal

Vertically opposite angles are equal

Calculations

\(\angle\)\({110}^\circ\) = \(\angle\)p   (Vertically opposite angles )

\(\angle\)p + \(\angle\)r1 +\(\angle\)r2 + \(\angle\)\({110}^\circ\) = \({360}^\circ\)

⇒ \(\angle\)\({110}^\circ\) + \(\angle\)r1 +\(\angle\)r2 + \(\angle\)\({110}^\circ\) = \({360}^\circ\)  (\(\angle\)r1 and \(\angle\)r2 are vertically opposites)

⇒ 2\(\angle\)r1 = \({140}^\circ\)

⇒ \(\angle\)r1 = \({70}^\circ\)

Now, \(\angle\)r1 = \(\angle\)a  (Corresponding angles)

\(\angle\)a = \({70}^\circ\)

Also, \(\angle\)a + \(\angle\)b = \({180}^\circ\)  (supplementary angles)

⇒ \(\angle\)b = \({180}^\circ\) - \({70}^\circ\) = \({110}^\circ\)

Therefore, the angles a and b are \({70}^\circ\) and \({110}^\circ\) respectively.