By description the quadrilateral must be an isosceles trapezoid in which the diagonal is equal to the larger base...just sketch it and you will see immediately that this is so.
Then mark the sides which are equal and the angles which are equal because there is an isosceles triangle within the isosceles trapezoid, it will quickly become evident that that the base angles of the trapezoid are 72 degrees and the other angles are 108 degrees.
Note: the isosceles triangle involved here turns out to be an interesting one. The ratio of the side to the base is the so-called "golden ratio". The vertices of this triangle fall on 3 of the vertices of a regular pentagon, i.e. you can use this triangle to construct a regular pentagon. To construct this triangle you need to know how to construct a rectangle with the sides in the ratio of the golden ratio. This paragraph will give you some clues to some interesting plane geometry if you are interested. Additionally check out Ptolemy's theorem.
