Question

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

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is B

let the angles be

$\angle$y = 3a, $\angle$z = 7a;

also $\angle$QRE and $\angle$QRF form a linear pair

So, $\angle$QRE + $\angle$z =${180}^{\circ }$

$\angle$QRE = ${180}^{\circ }$ - $\angle$z = ${180}^{\circ }$ - 7a

Also $\angle$y = $\angle$QRE (Corresponding angles)

3a = ${180}^{\circ }$ - 7a

10a = ${180}^{\circ }$

a = ${18}^{\circ }$

$\angle$y = 3 × a = 3 × ${18}^{\circ }$ = ${54}^{\circ }$

Also $\angle$APQ and $\angle$CQP are co - interior angles. (since AB || CD || EF)

$\angle$x + $\angle$y = ${180}^{\circ }$

$\angle$x + ${54}^{\circ }$ = ${180}^{\circ }$

$\angle$x = ${126}^{\circ }$