Do adjacent supplementary angles form a linear pair?

Yes, adjacent supplementary angles always form a linear pair.

Explanation:

• Adjacent angles are two angles that:
  • Share a common vertex
  • Have a common arm
  • Do not overlap
• Supplementary angles are two angles whose sum is 180°.
• A linear pair of angles is a pair of:
  • Adjacent angles, and
  • Angles whose non-common arms form a straight line

Therefore:

If two angles are:

• Adjacent (side by side, sharing a common vertex and arm)
• Supplementary (sum = 180°)

Then they must form a linear pair, because the two angles lie on a straight line.

 Example:

If ∠AOB = 120° and ∠BOC = 60°, and ray OB is the common arm:

• ∠AOB and ∠BOC are adjacent (common vertex and arm)
• They are supplementary (120° + 60° = 180°)
• ⇒ So, they form a linear pair.

Final Answer:

Yes, adjacent supplementary angles always form a linear pair because their non-common arms form a straight line and their sum is 180 degrees.