Question

Three parallelograms are hinged at each vertex to create an arm that can extend and collapse for an exploratory spaceship robot. What is m<1?

Answer 1

Given:

Three parallelograms are hinged at each vertex.

To find:

The measure of angle 1.

Solution:

From the given figure it is clear that angle on the vertex = 122°.

Now let angle 2 be the vertex angle in second parallelogram as shown in below figure.

$m\angle 2=122^\circ$              (Vertically opposite angles)

Two consecutive angles of a parallelogram are supplementary angles.

$m\angle 1+m\angle 2=180^\circ$

$m\angle 1+122^\circ=180^\circ$

$m\angle 1=180^\circ-122^\circ$

$m\angle 1=58^\circ$

Therefore, the measure of angle 1 is 58°.