Question

use the diagram to answer questions 2 - 5.

1. name the pairs of vertical angles in the figure.
2. which two angles are supplementary?
3. name an angle in the figure that is adjacent to angle 2.
4. which pairs of angles are complementary?

6.

Explanation:

Step1: Vertical angles

Vertical angles are opposite angles formed by the intersection of two lines. In the figure, \(\angle1\) and \(\angle3\) are opposite each other, and \(\angle5\) and \(\angle2\) are opposite each other.

Step2: Supplementary angles

Supplementary angles add up to \(180^{\circ}\). \(\angle1\) and \(\angle6\) form a linear pair (they are adjacent and their non - common sides form a straight line), so \(\angle1+\angle6 = 180^{\circ}\). Similarly, \(\angle2\) and \(\angle3\) form a linear pair (\(\angle2+\angle3=180^{\circ}\)), \(\angle3\) and \(\angle4\) form a linear pair (\(\angle3 + \angle4=180^{\circ}\)), \(\angle4\) and \(\angle5\) form a linear pair (\(\angle4+\angle5 = 180^{\circ}\)), \(\angle5\) and \(\angle6\) form a linear pair (\(\angle5+\angle6=180^{\circ}\)), \(\angle6\) and \(\angle1\) form a linear pair (already mentioned), \(\angle1\) and \(\angle2\) (if we consider the larger angles around the intersection of the lines in a different way of looking at adjacent angles on a straight - line - like structure formed by the intersection of multiple lines) can also be considered as supplementary in some geometric interpretations (since the sum of angles around a point is \(360^{\circ}\) and adjacent angles on a 'virtual' straight line formed by the intersection of lines sum to \(180^{\circ}\)).

Step3: Adjacent to \(\angle2\)

Adjacent angles have a common side and a common vertex. \(\angle3\) shares a common side and vertex with \(\angle2\).

Step4: Complementary angles

Complementary angles add up to \(90^{\circ}\). \(\angle1\) and \(\angle5\) (if we assume that the right - angle - like structure formed by the intersection of lines gives us that \(\angle1+\angle5 = 90^{\circ}\) based on the geometric configuration of the figure where there is a right - angle symbol near \(\angle1\) and \(\angle5\) in terms of their combined measure relative to the intersection of lines). Also, \(\angle1\) and \(\angle6\) (if we consider a different right - angle - like combination, but no, wait, no. Wait, if we assume that the intersection of lines creates a right - angle situation for \(\angle1\) and \(\angle5\) (maybe due to a perpendicular intersection in the figure's implied geometry) and also \(\angle6\) and \(\angle2\) (if we re - evaluate the angle sums based on the figure's structure where adjacent angles to a right - angle - like part sum to \(90^{\circ}\) in a different pair).

Answer:

1. \(\angle1\) and \(\angle3\), \(\angle2\) and \(\angle5\)
2. \(\angle1\) and \(\angle6\), \(\angle2\) and \(\angle3\), \(\angle3\) and \(\angle4\), \(\angle4\) and \(\angle5\), \(\angle5\) and \(\angle6\), \(\angle1\) and \(\angle2\)
3. \(\angle3\)
4. \(\angle1\) and \(\angle5\), \(\angle6\) and \(\angle2\)