Question

if these two figures are similar, what is the measure of the missing angle? 73° 107° 107° 73° ?

Explanation:

Step1: Recall similar polygons property

Corresponding angles of similar figures are equal.

Step2: Identify matching angle

The missing angle corresponds to either $73^\circ$ or $107^\circ$. Observe the shape: the smaller figure's missing angle matches the $73^\circ$ angles in the larger trapezoid (or alternatively, confirm total interior angles: for quadrilaterals, sum is $360^\circ$. $73+107+107+73=360$, so the missing angle must be one of the existing angles, and by similarity, it is $73^\circ$ or $107^\circ$; based on the shape's orientation, it is $73^\circ$).

Answer:

$73^\circ$