Questions: Question 16 of 44 If polygon A is a parallelogram, and polygon B is a rectangle, which of the following is true? A. Polygon A and B are parallelograms so neither can be circumscribed by a circle. B. Both polygon A and B are quadrilaterals, therefore a circle can circumscribe either one. C. Polygon A can be circumscribed by a circle because opposite sides must be supplementary. D. Polygon B represents the only parallelogram that a circle can circumscribe because opposite angles are supplementary.

Question 16 of 44 If polygon A is a parallelogram, and polygon B is a rectangle, which of the following is true?

A. Polygon A and B are parallelograms so neither can be circumscribed by a circle. B. Both polygon A and B are quadrilaterals, therefore a circle can circumscribe either one. C. Polygon A can be circumscribed by a circle because opposite sides must be supplementary. D. Polygon B represents the only parallelogram that a circle can circumscribe because opposite angles are supplementary.

Transcript text: Question 16 of 44 If polygon $A$ is a parallelogram, and polygon $B$ is a rectangle, which of the following is true? A. Polygon $A$ and $B$ are parallelograms so neither can be circumscribed by a circle. B. Both polygon $A$ and $B$ are quadrilaterals, therefore a circle can circumscribe either one. C. Polygon A can be circumscribed by a circle because opposite sides must be supplementary. D. Polygon $B$ represents the only parallelogram that a circle can circumscribe because opposite angles are supplementary.

Solution

Solution Steps

Step 1: Analyze polygon A

Polygon A is a parallelogram. Since adjacent angles in a parallelogram are supplementary, angles X and W are supplementary, as are angles Y and Z. Since angles X and Z are both 35°, angles W and Y must both be 180° - 35° = 145°. A quadrilateral can be circumscribed by a circle if and only if opposite angles are supplementary. In polygon A, angles X + Y = 35° + 145° = 180° and W + Z = 145° + 35° = 180°. Therefore, polygon A can be circumscribed by a circle.

Step 2: Analyze polygon B

Polygon B is a rectangle. All angles in a rectangle are 90°. A quadrilateral can be circumscribed by a circle if and only if opposite angles are supplementary. In polygon B, angles A + C = 90° + 90° = 180° and B + D = 90° + 90° = 180°. Therefore, polygon B can be circumscribed by a circle.

Step 3: Analyze the answer choices

A is incorrect. B is incorrect. C is partially correct; polygon A _can_ be circumscribed, but the reasoning is incorrect. D is incorrect.