Question

Amisha makes a star with the help of line segments a, b, c, d, e and f in which $a||d,$ $b||e$ and $c||f.$ Chhaya marks an angle as ${120}^{\circ }$ as shown in the given figure and asks Amisha to find $\angle x,\angle y$ and $\angle z.$ Help Amisha in finding the angles.

Answer 1

From the given figure, we have
$\angle a={120}^{\circ }\left[verticallyoppositeangles\right]$
Now, $\angle x+\angle a={180}^{\circ }[co-interiorangles]\Rightarrow \angle x+{120}^{\circ }={180}^{\circ }\Rightarrow \angle x={180}^{\circ }-{120}^{\circ }={60}^{\circ }$

Again, $\angle x=\angle 1\left[alternateinteriorangles\right]\Rightarrow {60}^{\circ }=\angle 1$
Also $\angle 1+\angle y={180}^{\circ }\Rightarrow {60}^{\circ }+\angle y={180}^{\circ }\left[linearpair\right]\Rightarrow \angle y={180}^{\circ }-{60}^{\circ }={120}^{\circ }$
Also, $\angle z+\angle a={180}^{\circ }[co-interiorangles]\Rightarrow \angle z+{120}^{\circ }={180}^{\circ }\Rightarrow \angle z={180}^{\circ }-{120}^{\circ }={60}^{\circ }$