Question

In the figure (not drawn to scale), $AGB,CGD$ and $EGF$ are straight lines. Find $\angle y$.

• A. ${97}^{\circ }$
• B. ${127}^{\circ }$
• C. ${100}^{\circ }$
• D. ${117}^{\circ }$

Answer 1

Answer: (D)

${117}^{\circ }$

$\angle CGE+\angle EGB+\angle BGD={180}^{\circ }$ (Angles on a straight line)
$\therefore {25}^{\circ }+\angle EGB+{38}^{\circ }={180}^{\circ }$
$\angle EGB={180}^{\circ }-({25}^{\circ }+{38}^{\circ })={180}^{\circ }-{63}^{\circ }={117}^{\circ }$
And $\angle y=\angle EGB$ (vertically opposite angles)
$\therefore \angle y={117}^{\circ }$.