Answer
$\theta_{1}$ = 60 degrees
$\theta_{2}$ = 1 rad = 57.33 degrees
$\theta_{1}$ - $\theta_{2}$ = 2.67 degrees
Work Step by Step
In the given triangle, each side is of length '1', hence it is an equilateral triangle. We know that each angle of an equilateral triangle is of 60 degrees. Therefore-
$\theta_{1}$ = 60 degrees
Now, after the rod is bent, it forms a sector with center angle $\theta_{2}$ and radius '1' and length of arc(i.e. length of rod) also remains '1'. Therefore-
Angle, $\theta_{2}$ = $\frac{arc}{radius}$ = $\frac{1}{1}$ = 1 rad
or, $\theta_{2}$ = $(1\times \frac{180}{\pi})$ degrees = 57.33 degrees
$\theta_{1}$ - $\theta_{2}$ = 60 - 57.33 = 2.67 degrees
