Question

if these two figures are similar, what is the measure of the missing angle? 43° 137° 137° 43° ?

Explanation:

Step1: Recall similar figures property

Similar figures have congruent corresponding angles.

Step2: Identify parallelogram angle pairs

The first figure is a parallelogram, with angles $43^\circ$ and $137^\circ$. The second figure is a similar parallelogram, so its angles match the first.

Answer:

The missing angle is either $43^\circ$ or $137^\circ$ (corresponding to the matching angle in the similar parallelogram; if the unknown angle corresponds to the acute angle, it is $43^\circ$, if to the obtuse angle, it is $137^\circ$). For a parallelogram, the two distinct angles are $43^\circ$ and $137^\circ$, so these are the possible measures.