Question

for safety and strength, the supports of a set of scissor steps form parallelograms. what should the measure of ∠1 be to allow a dog to climb safely into its owner’s car? the angles at the top right of the parallelograms in the arm are because they are by the ∠1 is to these angles, so m∠1 = (do not include the degree symbol in your answer.)

Explanation:

Step1: Recall parallelogram angle properties

In a parallelogram, opposite angles are equal, and consecutive angles are supplementary. Also, alternate interior angles are equal when lines are parallel (from the parallel sides of the parallelogram). The given angle is \(99^\circ\), and \(\angle 1\) and the \(99^\circ\) angle are alternate interior angles (since the sides of the parallelogram are parallel), so they are equal.

Step2: Determine \(m\angle 1\)

Since \(\angle 1\) and the \(99^\circ\) angle are equal (alternate interior angles, or opposite angles in parallelogram, but here alternate interior is more direct from the diagram's parallel sides), \(m\angle 1 = 99\).

Answer:

99