Question

Which are valid pairs of opposite angle measures for a quadrilateral inscribed

in a circle? Select all that apply.
0
A. 68%, 122°
B. 90°, 90°
C. 71°, 111°
D. 54°, 126

Answer 1

For a quadrilateral inscribed in a circle, the opposite angles must sum up to 180°, making options B (90°, 90°) and D (54°, 126°) the valid pairs.

The question asks which pairs of opposite angle measures are valid for a quadrilateral inscribed in a circle. According to the theorem regarding circles, the opposite angles of a quadrilateral inscribed in a circle must sum up to 180°. This rule is often known as the inscribed quadrilateral theorem.

For option A (68°, 122°), the sum is 68° + 122° = 190°, which is not equal to 180°, hence it's invalid.

Option B (90°, 90°) sums up to 90° + 90° = 180°, making it a valid pair as they are opposite angles of a rectangle.

Option C (71°, 111°) results in 71° + 111° = 182°, not equal to 180°, therefore it's invalid.

For option D (54°, 126°), the sum is 54° + 126° = 180°, which is valid.

Hence, the valid pairs are B (90°, 90°) and D (54°, 126°).