Student wrote:

When you state that "the relation between the angle CAB and the angle DOE is:angle DOE + angle CAB = 180°" please confirm that you know this because angles ADO and OEA each are 90° (which we know because ADC and AEB are each perpendicular to the radii bc inscribed) leaving 180 remaining degrees of the quadrilateral.

That is correct.

**Quote:**

Also, is there any other way to solve this problem without identifying the quadrilateral?

I see no clearer way to solve this question. Basically, we've solved it in two steps:

1. The sum of all angles in the quadrilateral is 360°.

2. One of the angles is given, 60°. Another two are 90°, because of the tangent lines. So the remaining angle is 360° - 90° - 90° - 60° = 120°.

If you didn't know the property of angles in a quadrilateral (that they sum up to 360⁰), then you could divide the quadrilateral into two triangles. It can be divided either into two equal right triangles, or into two isosceles triangles, depending on which diagonal you draw. In each case you would also need to use the fact that tangent lines make 90⁰ angles with the radii.