The picture below is cross-section of an optical fibre cable used to let light travel through by bouncing off its walls. However, only the portion light entering with in a range of angles will be able to make it to the other end. 

To prevent the light escape through the wall of the OFC cable, the angle measure, $y$ (shown in the figure) must be greater than $61°$.

What should be range of angle measures for $x$ (shown in the figure) that make it possible?

Two interstate highways of uniform widths $30 \mathrm{m}$ and $45 \mathrm{m}$ intersect at $55°$ angle as shown below.

What is the measure of angle marked in the figure?

The term, bearing is used to mention the angle relative to the North in clockwise direction. If the bearing is $0°$ it is due North. Similarly $90°, 180°, 270°$ bearing angles are due East, South, and West respectively.

A ship travelled from location $A$ on a bearing $20°$ and on reaching location $B$ it changed its navigation on a bearing $90°$.  When it reached $C$ its bearing changed to $140°$ till it reached location $D.$ Now the ship needs to travel back to its original location, $A$, on a bearing of $280°$. 

What is the measure of $\angle BAD$?