Question

In the given figure measure of some angles are given. Using the measures find the value of $x,y,z.$

Answer 1

In the given figure,

$\angle NMT+\angle RMT={180}^{\circ }$ ......(1)

$\angle RMT={140}^{\circ },\angle NMT=z$,

Substituting in equation(1),

${140}^{\circ }+z={180}^{\circ }$ $\Rightarrow$ $z={40}^{\circ }$,

Now,

Using exterior angle theorem when $\angle NET={100}^{\circ }$ is an exterior angle,

$x+z={100}^{\circ }$

$x+{40}^{\circ }={100}^{\circ }$$\Rightarrow$ $x={60}^{\circ }$

Now, In $△ENM,$

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

$y+{100}^{\circ }={180}^{\circ }$$\Rightarrow$ $y={80}^{\circ }$