Question

If polygon A is a parallelogram, and polygon B is a rectangle, which of the

Answer 1

Answer:

The answer is C

Step-by-step explanation:

* Lets talk about some facts in parallelograms and rectangles

- Rectangle is a parallelogram with right angles

- Supplementary angles is two angles their sum is 180°

- The opposite angles in the rectangle are equal and supplementary

- A circle can circumscribe a quadrilateral if the opposite angles of

 the quadrilateral are supplementary

- In the parallelograms opposite angles are equal

- The circle can circumscribe a rectangle because its opposite

 angles are supplementary

- The circle can't circumscribe a parallelogram because its opposite

 angles are not supplementary they are equal

* Lets solve the problem

- Polygon A is a parallelogram

- Polygon B is a rectangle (parallelogram with right angles)

∵ The circle can't circumscribe a parallelogram because its opposite

  angles are not supplementary

∴ Polygon A can't circumscribed by a circle

∵ Polygon B is a rectangle its opposite angles are equal the measure

  of  each one is 90°

∴ Its opposite angles are supplementary

∴ Polygon B can circumscribed by a circle

∵ The rectangle is a parallelogram with right angles

∴ Polygon B represents the only parallelogram that a circle can

  circumscribed because opposite angles are supplementary

* The answer is C