Complete the following theorem statements below:
8.1.1 The angle between a tangent and a chord is …
8.1.2 The exterior angle of a cyclic quadrilateral is equal to …

The angle between a tangent and a chord is equal to the angle subtended by the chord on the opposite arc. This means if you have a tangent line touching a circle at one point and a line segment (the chord) drawn from that point to another point on the circle, the angle formed between the tangent and the chord is equivalent to the angle that the chord creates with a line drawn from one end of the chord, going on the circle’s arc to the other end.

The exterior angle of a cyclic quadrilateral is equal to the sum of the two opposite interior angles. In simple terms, if you imagine a four-sided figure inscribed within a circle, then any angle formed outside the quadrilateral will be equal to the total measure of the angles that are not adjacent to it within the figure. It’s a neat little trick to keep in your back pocket during geometry proofs!