Question

To make sure that a given parallelogram is a rectangle, at least how many of its angles must measure 90?

Answer 1

Answer:

The answer is 1 side must measure 90

Step-by-step explanation:

Answer 2

To make sure that a parallelogram is a rectangle, we need at least one angle measure 90°.

What is a parallelogram?

A quadrilateral with opposing sides parallel is known as a parallelogram (and therefore opposite angles are equal). A rhombus is a quadrilateral with equal sides, whereas a rectangle is a parallelogram whose angles are all right angles.

How are angles of a parallelogram related?

A parallelogram is a flat two-dimensional form with four angles. The inner angles opposite each other are equal. The transversal angles on the same side are supplementary, meaning they sum up to 180 degrees. As a result, the total of a parallelogram's internal angles equals 360 degrees.

How do we solve the given question?

We are asked the minimum number of right angles (90°), for a parallelogram to be a rectangle.

Let the given parallelogram be ABCD. For a parallelogram to be a rectangle, all its angles need to be 90°. Let ∠A = 90°.

∴∠C = ∠A = 90°. (∵ Opposite angles of a parallelogram are equal)

∠A + ∠B = 180°. (∵ Adjacent angles are supplementary, that is, their sum is 180°)

⇒∠B = 180°- ∠A = 180° - 90° = 90°

∴∠D = ∠B = 90°. (∵ Opposite angles of a parallelogram are equal)

∴ All four angles are right angles (90°), given one angle = 90°.

∴ To make sure that a parallelogram is a rectangle, we need at least one angle measure 90°.

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