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, \(\angle1+\angle2 = 180^{\circ}\).
• 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, \(\angle1\) and \(\angle3\) are formed by the intersection of two lines (line \(l\) and line \(m\) with the transversal).

Answer:

(a) Supplementary angles: \(\angle1\) and \(\angle2\)
(b) Vertical angles: \(\angle1\) and \(\angle3\)