Question

select the correct answer
prove: if two angles are supplementary, they also form a linear pair.
which image provides the best counterexample for this statement?
a.
image of angle 1 and angle 2 forming a linear pair
b.
image of two non - adjacent angles
c.
image of two angles in a right angle
d.
image of two separate angles

Explanation:

To find a counterexample, we need two supplementary angles (sum to \(180^\circ\)) that do NOT form a linear pair (linear pairs are adjacent and form a straight line).

• Option A: Angles 1 and 2 are adjacent, form a straight line (linear pair) and are supplementary. Not a counterexample.
• Option B: Angles 1 and 2 are non - adjacent, but we need to check if they are supplementary. From the diagram, angle 1 looks like an acute angle in a triangle (maybe \(45^\circ\)) and angle 2 looks like an obtuse angle (maybe \(135^\circ\)), so they are supplementary (\(45 + 135=180\)) and not a linear pair (not adjacent, no common side/vertex forming a line). This fits a counterexample.
• Option C: Angles 1 and 2 are complementary (sum to \(90^\circ\)), not supplementary.
• Option D: Angles 1 and 2 are likely acute and not supplementary.

Answer:

B. The image with angle 1 in a triangle - like figure and angle 2 as an obtuse - angled figure (non - adjacent, supplementary, not a linear pair)