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AOB is a straight line, and rays OC and OD start from O as shown. Which pair of angles is adjacent but NOT a linear pair?

Class 7Lines and AnglesLines and Angles
  • A∠AOC and ∠COB
  • B∠AOD and ∠DOB
  • C∠AOC and ∠DOB
  • D∠AOC and ∠COD

Step-by-Step Solution

∠AOC and ∠COD share the arm OC and the vertex , so they are adjacent, but their outer arms and do not make a straight line . ∠AOC + ∠COB and ∠ + ∠DOB are linear pairs, and ∠AOC, ∠DOB share no arm.
Answer: D) ∠AOC and ∠COD

Key idea: Linear pair

When two adjacent angles share a side, and their other sides together form a straight line, they make a **linear pair**. The two angles always sum to 180°.

If you know one of a linear pair, you can find the other by subtracting from 180°.

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