Question

1. which of these diagrams shows a pair of supplementary angles? a b c d

Explanation:

To determine which diagram shows supplementary angles, we recall that supplementary angles are two angles whose sum is \(180^\circ\) (a straight angle).

Step 1: Analyze Diagram A

Diagram A shows two angles that do not form a straight line. Their sum is not \(180^\circ\).

Step 2: Analyze Diagram B

Diagram B has a straight line (the vertical line) with two angles (green and blue) forming a straight angle. A straight angle is \(180^\circ\), so these two angles are supplementary.

Step 3: Analyze Diagram C

Diagram C shows a right angle (the purple square) and two other angles. The sum of the angles here is related to a right angle (\(90^\circ\)) or less, not \(180^\circ\).

Step 4: Analyze Diagram D

Diagram D shows angles that do not form a straight line. Their sum is not \(180^\circ\).

Answer:

B. Diagram B (the one with the vertical straight line and two angles forming a straight angle)