Which set of measures describes a quadrilateral that cannot be inscribed in a circle 69 103 111 77 or 52 64 128 116 or 42 64 118 136 or 100 72 80 108?

Answer 1

A quadrilateral can be inscribed in a circle if the opposite angles are supplementary. To determine which set of measures cannot form a cyclic quadrilateral, we calculate the sums of opposite angles for each set. The set of angles 100, 72, 80, and 108 has opposite angle pairs (100 + 80 = 180 and 72 + 108 = 180), which are supplementary. However, the other sets do not all yield supplementary pairs, with 42, 64, 118, and 136 failing this condition. Thus, 42, 64, 118, and 136 describe a quadrilateral that cannot be inscribed in a circle.