Question

In the figure (not drawn to scale), $AJE,BJF,CJG$ and $DJH$ are straight lines.
Find $\angle x$ and $\angle y$ respectively.

• A. ${50}^{\circ },{49}^{\circ }$
• B. ${59}^{\circ },{40}^{\circ }$
• C. ${59}^{\circ },{59}^{\circ }$
• D. ${49}^{\circ },{48}^{\circ }$

Answer 1

The correct option is C ${59}^{\circ },{59}^{\circ }$

(a) As, $\angle AJB+\angle BJC+\angle CJD+\angle DJE={180}^{\circ }$ (Angles on a straight line $AE$)
$\therefore {42}^{\circ }+\angle x+{40}^{\circ }+{39}^{\circ }={180}^{\circ }$
$\angle x={180}^{\circ }-({42}^{\circ }+{40}^{\circ }+{39}^{\circ })$
$\angle x={180}^{\circ }-{121}^{\circ }={59}^{\circ }$
(b) $\angle y=\angle x$ (Vertically opposite angles)
$\therefore y={59}^{\circ }$.