Final answer:
Without additional information or a diagram, it is not possible to accurately determine the measures of angles Za, Zc, and Zh in the geometrical figure described. Assuming corresponding and supplementary angle relationships may apply, one can infer potential measures, but these are only speculative without visual confirmation.
Step-by-step explanation:
The given question pertains to the measurement of angles in a geometric figure, where m | n suggests that line m is parallel to line n, and m∠e = 102°. To determine the measure of ∠a, ∠c, and ∠h, we would typically use the properties of parallel lines and the angles formed by a transversal. However, without the figure or more context, it is not possible to provide the exact values of the angles. If additional information is available, such as the relationship between the angles, we can apply concepts like corresponding angles, alternate interior angles, and supplementary angles to find the measures of these angles.
If m∠e is given as 102° and if we assume that ∠a and ∠e are corresponding angles, then m∠a would also be 102° because corresponding angles are equal when lines are parallel. Similarly, if ∠c is a supplementary angle to ∠e, which is often the case if m and n are parallel and cut by a transversal, then m∠c would be 78° (since 180° - 102° = 78°). For ∠h, without specific information, we cannot determine its measure.