Question

three parallelograms are hinged at each vertex to create an arm that can extend and collapse for an exploratory spaceship robot. what is ( mangle1 )? explain how you found the answer. all of the angles along the corner of the parallelograms in the arm are ( square ) because they are either ( square ) or ( square ) angles of a parallelogram. by the ( square angle1 ) is ( square ) to these angles, so ( mangle1=square ) (do not include the degree symbol in your answer)

Explanation:

Step1: Properties of parallelogram angles

In a parallelogram, opposite angles are equal and consecutive angles are supplementary. Also, when parallelograms are hinged in this way, the angles along the corner of the parallelograms in the arm are congruent. They are either opposite or consecutive angles of a parallelogram. By the transitive property of congruence, \(\angle1\) is congruent to the given \(60^{\circ}\) angle.

Answer:

All of the angles along the corner of the parallelograms in the arm are congruent because they are either opposite or consecutive angles of a parallelogram. By the transitive property of congruence, \(\angle1\) is congruent to these angles, so \(m\angle1 = 60\)