3B. The angles of a quadrilateral in sequence are $x, x+20, x+30, x+50$. Determine its angles, and then prove that it is a trapezoid.
Solution. Since the sum of the angles in any quadrilateral is $360^{\circ}$, we get $x+x+20+x+30+x+50=360^{\circ}$, i.e., $x=65^{\circ}$. Therefore, the angles of the quadrilateral are $65^{\circ}, 85^{\circ}, 95^{\circ}, 115^{\circ}$. Since $85^{\circ}+95^{\circ}=115^{\circ}+65^{\circ}=180^{\circ}$, the pairs of angles $85^{\circ}, 95^{\circ}$ and $115^{\circ}, 65^{\circ}$ are angles on a transversal. Since these are angles in a quadrilateral, it is a trapezoid.