Question

7
multiple choice 1 point
in the figure shown, ( l_1 ) and ( l_2 ) are
not parallel.
which angles are supplements of ( angle 2 )?
angles 2 and 5
angles 4 and 8
angles 5 and 7
angles 6, 3, and 8

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two - angle pairs that sum to \(180^{\circ}\). Also, when two lines intersect, adjacent angles are supplementary.

Step2: Analyze the relationship between \(\angle2\) and \(\angle6\) with \(\angle5\)

• \(\angle2\) and \(\angle5\) are not adjacent to \(\angle6\) in a way that forms a linear - pair with \(\angle6\).
• \(\angle4\) and \(\angle8\) are not adjacent to \(\angle6\) in a way that forms a linear - pair with \(\angle6\).

Step3: Check the linear - pair relationship for \(\angle5\), \(\angle6\) and \(\angle7\)

• \(\angle5+\angle6 = 180^{\circ}\) (they form a linear pair as they are adjacent and lie on a straight line along \(l_1\)).
• \(\angle6+\angle7 = 180^{\circ}\) (they form a linear pair as they are adjacent and lie on a straight line along the transversal that intersects \(l_1\) and \(l_2\)).

Step4: Analyze the option with three angles

Angles \(\angle6\), \(\angle3\), and \(\angle8\) do not follow the supplementary - angle (two - angle) definition.

Answer:

Angles \(5\) and \(7\) (the option "Angles \(5\) and \(7\)" is the correct one)