Question

Each list shows the interior angle measures of a quadrilateral. Which set of measures describes a quadrilateral that cannot be inscribed in a circle?

69°, 103°, 111°, 77°

52°, 64°, 128°, 116°

42°, 64°, 118°, 136°

100°, 72°, 80°, 108°

Answer 1

C. 42°, 64°, 118°, 136°.

Explanation:

Answer 2

We have to choose which set of measures describes a quadrilateral that can not be inscribed in a circle. An inscribed quadrilateral has vertices that lie on a circle. The sum of the opposite angles of such quadrilateral is 180° ( the angles are supplementary ). Answer A: 103° + 77° = 180°, 69° + 111° = 180°. Answer B : 52° + 128° = 180°, 64° + 116° = 180°. Answer C: 42° + 136° = 178°, 64° + 118°=182° ( not complementary ). Answer D : 100° + 80° = 180° , 72° + 108° = 180°. Answer : C. 42°, 64°, 118°, 136°.