Question

Find angles $x$ and $y$, as show in the figure.

[2 marks]

Answer 1

In $△ABC$,
$x=60{}^{\circ }$ [vertically oppposite angles]
[0.5 mark]

Now, by angle sum property
$\Rightarrow x+y+30{}^{\circ }=180{}^{\circ }$
$\Rightarrow 60{}^{\circ }+y+30{}^{\circ }=180{}^{\circ }$
$\Rightarrow 90{}^{\circ }+y=180{}^{\circ }$
$\Rightarrow y=180{}^{\circ }-90{}^{\circ }$
$\Rightarrow y=90{}^{\circ }$
[1.5 marks]

Thus, the values of $x$ and $y$ are $60{}^{\circ }$ and $90{}^{\circ }$ respectively.