for the figure below, give the following. (a) one pair of vertical angles (b) one pair of angles that form a…

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 ∠

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 ∠

Answer

Explanation:

Step1: Recall vertical - angle definition

Vertical angles are opposite angles formed by the intersection of two lines. In the given figure, when line (n) intersects line (l), (\angle1) and (\angle4) are vertical angles.

Step2: Recall linear - pair definition

A linear pair of angles are adjacent angles that form a straight line. (\angle1) and (\angle2) form a linear pair since they are adjacent and their non - common sides form a straight line.

Step3: Recall congruent - angle cases

Vertical angles are congruent. So, (\angle1) and (\angle4) are congruent. Also, corresponding angles (e.g., (\angle1) and (\angle5)) are congruent when the lines (l) and (m) are parallel. Let's use vertical angles for congruent pair here.

Answer:

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