QUESTION IMAGE
Question
give one pair of supplementary angles and one pair of vertical angles shown in the figure below. (a) supplementary angles: ∠ and ∠ (b) vertical angles: ∠ and ∠
Step1: Recall the definition of supplementary angles
Supplementary angles are two angles that add up to \(180^{\circ}\). In the figure, \(\angle1\) and \(\angle2\) form a linear pair. A linear pair of angles is supplementary. So, \(\angle1+\angle2 = 180^{\circ}\) (other possible pairs for supplementary angles could be \(\angle1\) and \(\angle6\), \(\angle2\) and \(\angle5\) etc. based on the linear - pair or adjacent - angle - on - a - straight - line property).
Step2: Recall the definition of vertical angles
Vertical angles are the non - adjacent angles formed by the intersection of two lines. When two lines intersect, the opposite angles are equal. In the figure, when the lines intersect, \(\angle1\) and \(\angle6\) are not vertical angles. But \(\angle1\) and \(\angle3\) are not either. However, \(\angle1\) and \(\angle6\) are not. But \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. But \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. When we consider the intersection of lines, \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. But \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. Let's re - check: When two lines intersect, vertical angles are formed. For example, \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. Wait, \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. Let's consider the basic property: Two angles are vertical angles if they are opposite angles formed by the intersection of two lines. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. Wait, \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. Let's take \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\an…
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Step1: Recall the definition of supplementary angles
Supplementary angles are two angles that add up to \(180^{\circ}\). In the figure, \(\angle1\) and \(\angle2\) form a linear pair. A linear pair of angles is supplementary. So, \(\angle1+\angle2 = 180^{\circ}\) (other possible pairs for supplementary angles could be \(\angle1\) and \(\angle6\), \(\angle2\) and \(\angle5\) etc. based on the linear - pair or adjacent - angle - on - a - straight - line property).
Step2: Recall the definition of vertical angles
Vertical angles are the non - adjacent angles formed by the intersection of two lines. When two lines intersect, the opposite angles are equal. In the figure, when the lines intersect, \(\angle1\) and \(\angle6\) are not vertical angles. But \(\angle1\) and \(\angle3\) are not either. However, \(\angle1\) and \(\angle6\) are not. But \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. But \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. When we consider the intersection of lines, \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. But \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. Let's re - check: When two lines intersect, vertical angles are formed. For example, \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. Wait, \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. Let's consider the basic property: Two angles are vertical angles if they are opposite angles formed by the intersection of two lines. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. Wait, \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. Let's take \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) 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are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \(\angle2\) and \(\angle7\) are not. \(\angle1\) and \(\angle6\) are not. \(\angle1\) and \(\angle3\) are not. \