Respuesta :

The given parallelogram is a rhombus

Solution:

Option A: Rhombus

Let us recall the property of rhombus.

  • Diagonals bisect each other at right angles.
  • Opposite angles are congruent.

Here diagonals bisect the angles equally each 72°.

Opposite angles are congruent(72° + 72° = 144°).

Hence the given parallelogram is a rhombus.

Option B: Rectangle

Let us recall the property of rectangle.

  • Diagonals bisect each other.
  • All the angles of a rectangle are 90°.

Here 72° + 72° = 144°, not 90°.

So, the given parallelogram is not a rectangle.

Option C: Square

Let us recall the property of square.

  • Diagonals bisect each other.
  • All the angles of a square are 90°.

Here 72° + 72° = 144°, not 90°.

So, the given parallelogram is not a square.

akposevictor

The parallelogram with the given angle measures is a rhombus.

Some Properties of a Rhombus

  • In a rhombus, the angles that are directly opposite each other are equal in measure (congruent).
  • A diagonal of a rhombus bisects angles thereby dividing the angle into equal parts.

In the parallelogram given:

  • The opposite angles are equal - (72 + 72) = (72 + 72)
  • The diagonal bisects the angles into equal parts - 72° each.

Therefore, the parallelogram with the given angle measures is a rhombus.

Learn more about rhombus on:

https://brainly.com/question/20627264

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