Originally Posted by

**Prove It** A rectangle is DEFINED to be a four sided polygon with all angles congruent.

The angle sum of a polygon of "n" sides is $\displaystyle \displaystyle \begin{align*} (n - 2) \cdot 180^{\circ} \end{align*}$. So for a quadrilateral, the angle sum is $\displaystyle \displaystyle \begin{align*} (4 - 2)\cdot 180^{\circ} = 360^{\circ} \end{align*}$.

Since all the angles are equal, that means if "a" is one of the angles, then $\displaystyle \displaystyle \begin{align*} 4a= 360^{\circ} \implies a = 90^{\circ} \end{align*}$.

Therefore, the angles in a rectangle are all right angles.