Question

In the adjoining figure, $p\parallel q$. The unknown angles are

• A. $a={55}^{\circ },b={225}^{\circ }$
  $c={45}^{\circ },d={25}^{\circ },e={65}^{\circ },f={55}^{\circ }$
• B. $a={55}^{\circ },b={125}^{\circ }$
  $c={55}^{\circ },d={125}^{\circ },e={55}^{\circ },f={55}^{\circ }$
• C. $a={35}^{\circ },b={25}^{\circ }$
  $c={75}^{\circ },d={225}^{\circ },e={50}^{\circ },f={60}^{\circ }$
• D. $a={45}^{\circ },b={130}^{\circ }$
  $c={55}^{\circ },d={135}^{\circ },e={55}^{\circ },f={50}^{\circ }$

Answer 1

The correct option is B $a={55}^{\circ },b={125}^{\circ }$

$c={55}^{\circ },d={125}^{\circ },e={55}^{\circ },f={55}^{\circ }$
Given parallel lines p, q are cut by a transversal line

$\because {125}^{\circ }+e={180}^{\circ }$ [Linear pair]

$\therefore e={180}^{\circ }-{125}^{\circ }={55}^{\circ }\left(i\right)$

$e=f=55$ [Vertically opposite angles]

$a=f=55$ [Alternate interior angles]

$a+b={180}^{\circ }$ [Linear pair]

$\Rightarrow {55}^{\circ }+b={180}^{\circ }$ [From eq. (i)]

$\Rightarrow b={180}^0-{55}^{\circ }={125}^{\circ }$

$a=c={55}^{\circ },b=d={125}^{\circ }$ [Vertically opposite angles]

$\Rightarrow a={55}^{\circ },b={125}^{\circ }$

$\therefore c={55}^{\circ },d={125}^{\circ },e={55}^{\circ },f={55}^{\circ }$.