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Ray OC lies between rays OA and OB, and ∠AOB is a straight angle. If ∠AOC is 5 times ∠COB, find ∠AOC.

Class 7Lines and AnglesLines and Angles
  • A150°
  • B30°
  • C36°
  • D144°

Step-by-Step Solution

Because ∠AOB is a straight angle, ∠AOC and ∠COB form a linear pair and sum to 180°. Let ∠COB = , so ∠AOC = . Then → → °, giving ∠AOC = 5 (30) = 150°. Trap: 30° is ∠COB, the smaller part; the question asks for ∠AOC.
Answer: A) 150°

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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