Question

puestos por el vértice y un par de ángulos suplementarios que se muestran en la figura adjacente. (a) ángulos opuestos por el vértice: ∠ y ∠ (b) ángulos suplementarios: ∠ y ∠

Explanation:

Step1: Recall vertex - opposite angles definition

Vertex - opposite angles are formed when two lines intersect. They are equal in measure. In the given figure, when two lines intersect, $\angle1$ and $\angle3$ are opposite - by - vertex angles, and also $\angle2$ and $\angle4$ are opposite - by - vertex angles.

Step2: Recall supplementary angles definition

Supplementary angles are two angles whose sum is $180^{\circ}$. In the figure, $\angle1$ and $\angle2$ are supplementary (they form a linear pair), also $\angle2$ and $\angle3$, $\angle3$ and $\angle4$, $\angle4$ and $\angle1$ are supplementary pairs.

Answer:

(a) $\angle1$ and $\angle3$; $\angle2$ and $\angle4$
(b) $\angle1$ and $\angle2$ (or $\angle2$ and $\angle3$, $\angle3$ and $\angle4$, $\angle4$ and $\angle1$)