Question

give one pair of supplementary angles and one pair of vertical angles shown in the figure below.
(a) supplementary angles: $angle square$ and $angle square$
(b) vertical angles: $angle square$ and $angle square$

Explanation:

Step1: Recall Supplementary Angles

Supplementary angles are two angles whose sum is \(180^\circ\). In the figure, \(\angle1\) and \(\angle2\) form a linear pair (they are adjacent and form a straight line), so their sum is \(180^\circ\). So one pair of supplementary angles can be \(\angle1\) and \(\angle2\).

Step2: Recall Vertical Angles

Vertical angles are opposite angles formed by the intersection of two lines. When two lines intersect, vertical angles are equal. For example, when the two lines (the vertical line and line \(l\)) intersect, \(\angle1\) and \(\angle4\) are vertical angles (or \(\angle2\) and \(\angle3\), or for the other intersection, \(\angle5\) and \(\angle8\), \(\angle6\) and \(\angle7\)). Let's take \(\angle1\) and \(\angle4\) as a pair of vertical angles.

Answer:

(a) Supplementary angles: \(\angle1\) and \(\angle2\) (other valid pairs: \(\angle2\) and \(\angle3\), \(\angle3\) and \(\angle4\), \(\angle4\) and \(\angle1\), \(\angle5\) and \(\angle6\), \(\angle6\) and \(\angle7\), \(\angle7\) and \(\angle8\), \(\angle8\) and \(\angle5\), etc.)
(b) Vertical angles: \(\angle1\) and \(\angle4\) (other valid pairs: \(\angle2\) and \(\angle3\), \(\angle5\) and \(\angle8\), \(\angle6\) and \(\angle7\))

(For the blanks, possible answers:
(a) \(\angle1\) and \(\angle2\) (or any linear pair)
(b) \(\angle1\) and \(\angle4\) (or other vertical angle pairs))

If we follow the first possible pairs:
(a) Supplementary angles: \(\angle1\) and \(\angle2\)
(b) Vertical angles: \(\angle1\) and \(\angle4\)