Question

In the given figure, find the values of the angles x, y, and z. [3 Marks]

Answer 1

Here, $z={40}^{\circ }$ [Vertically opposite angles] [0.5 Marks]

Now, ${40}^{\circ }$ + $y$ = ${180}^{\circ }$ [Linear pair]

$\Rightarrow y$ = ${180}^{\circ }-{40}^{\circ }$

$\Rightarrow y$ = ${140}^{\circ }$ [1 Mark]

Also,

${40}^{\circ }+x+{25}^{\circ }={180}^{\circ }$ [Angles on a straight line]

$\Rightarrow x+{65}^{\circ }={180}^{\circ }$

$\Rightarrow x={180}^{\circ }-{65}^{\circ }$

$\Rightarrow x={115}^{\circ }$ [1.5 Marks]

Thus, $x={115}^{\circ }$, $y$ = ${140}^{\circ }$ and $z={40}^{\circ }$