Question

for the figure below, give the following.
(a) one pair of vertical angles
(b) one pair of angles that form a linear pair
(c) one pair of angles that are congruent
(a) vertical angles: and
(b) linear pair: and
(c) congruent angles: and

Explanation:

• (a) Vertical angles: Vertical angles are opposite angles formed by two intersecting lines. In the figure, \(\angle1\) and \(\angle4\) are opposite each other (another possible pair could be \(\angle2\) and \(\angle3\), \(\angle5\) and \(\angle8\), or \(\angle6\) and \(\angle7\)).
• (b) Linear pair: A linear pair of angles is adjacent angles that form a straight line (sum to \(180^{\circ}\)). \(\angle1\) and \(\angle2\) are adjacent and form a straight - line along line \(l\) (another possible pair could be \(\angle3\) and \(\angle4\), \(\angle5\) and \(\angle6\), or \(\angle7\) and \(\angle8\)).
• (c) Congruent angles: Congruent angles have the same measure. Vertical angles are congruent. Since \(\angle1\) and \(\angle4\) are vertical angles, they are congruent (also, if lines \(l\) and \(m\) were parallel, there would be more congruent angle pairs due to the properties of parallel lines and transversals, but using the vertical - angle property is straightforward here).

Answer:

(a) \(\angle1\) and \(\angle4\)
(b) \(\angle1\) and \(\angle2\)
(c) \(\angle1\) and \(\angle4\)