Question

In the given figure, if AB || CD, CD || EF and y : z = 3 : 7, find x.

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}-->

• A. <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${72}^{\circ }$
• B. <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${108}^{\circ }$
• C. <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${126}^{\circ }$
• D. <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${96}^{\circ }$

Answer 1

The correct option is C <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${126}^{\circ }$

It is known that AB || CD and CD || EF

As the angles on the same side of a transversal line sums up to 180°,
x + y = 180° —–(i)

The vertically opposite angle of y will be supplementary with z, so y + z = 180°

Now, let y = 3w and hence, z = 7w (As y : z = 3 : 7)

∴ 3w + 7w = 180°
$\Rightarrow$ 10w = 180°
$\Rightarrow$ w = 18°

Now, y = 3 × 18° = 54°
and z = 7 × 18° = 126°

Now, angle x can be calculated from equation (i)
$\Rightarrow$ x + y = 180°
$\Rightarrow$ x + 54° = 180°
∴ x = 126°