Question

In the figure given below, If $AB\parallel CD$ and $CD\parallel EF$ and y : z = 3 : 7, find x. [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Marks
Answer: 1 Mark

Let the angles be $\angle y=3a,\angle z=7a$;

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

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

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

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

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

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

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

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

$\angle APQ$ and $\angle CQP$ are supplementary. (since $AB\parallel CD\parallel EF$)

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

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

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