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 ∠

Explanation:

• Supplementary angles: Two angles are supplementary if their sum is \(180^{\circ}\). In the figure, \(\angle1\) and \(\angle2\) form a linear - pair (they are adjacent and their non - common sides are opposite rays). By the linear - pair postulate, \(\angle1+\angle2 = 180^{\circ}\). Other possible pairs include \(\angle5\) and \(\angle6\), \(\angle3\) and \(\angle4\), \(\angle7\) and \(\angle8\), \(\angle1\) and \(\angle5\), \(\angle2\) and \(\angle6\) etc.
• Vertical angles: Vertical angles are a pair of non - adjacent angles formed by the intersection of two lines. When two lines intersect, the opposite angles are equal. For example, when the two lines intersect to form angles \(\angle1\) and \(\angle3\), \(\angle1\) and \(\angle3\) are vertical angles. Other pairs of vertical angles in the figure are \(\angle2\) and \(\angle4\), \(\angle5\) and \(\angle7\), \(\angle6\) and \(\angle8\).

Answer:

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