Question

in a parallelogram, the sum of the consecutive angles is ______.
90°
180°
270°
360°

Explanation:

Step1: Recall parallelogram properties

In a parallelogram, opposite sides are parallel. When two parallel lines are cut by a transversal, consecutive interior angles are supplementary (their sum is \(180^\circ\)). In a parallelogram, consecutive angles are formed by a side (transversal) cutting two parallel sides, so they are supplementary.

Step2: Evaluate options

• \(90^\circ\): Not supplementary, incorrect.
• \(180^\circ\): Matches the supplementary property of consecutive angles in a parallelogram.
• \(270^\circ\): Too large, not supplementary, incorrect.
• \(360^\circ\): Sum of all interior angles of a parallelogram, not consecutive angles, incorrect.

Answer:

\(180^\circ\) (the option with \(180^\circ\))