Angle between two chords

By ratio and proportion
$\dfrac{28}{\beta} = \dfrac{2\pi (10)}{360^\circ}$

$\beta = 160.43^\circ$
 

 

$\alpha = 360^\circ - \beta$

$\alpha = 360^\circ - 160.43^\circ$

$\alpha = 199.57^\circ$
 

$\theta = \frac{1}{2}\alpha$

$\theta = \frac{1}{2}(199.57^\circ)$

$\theta = 99.78^\circ$