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Four rays OA, OB, OC and OD are drawn from a point O. ∠AOB = 92°, ∠BOC = 108°, and ∠COD is 15° more than ∠AOB. Find ∠DOA.

Class 7Lines and AnglesLines and Angles
  • A68°
  • B127°
  • C53°
  • D73°

Step-by-Step Solution

Angles around a point add to 360°. First ∠COD = 92 + 15 = 107°. Then ∠DOA = 360 − (92 + 108 + 107) = 360 − 307 = 53°. Trap: 68° comes from forgetting the extra 15° and using 92° for ∠COD; 127° is the supplement of 53°, not the angle itself.
Answer: C) 53°

Key idea: Solving 'find the angle' problems

Most Class-7 angle problems give you one or two angle measures and ask you to find an unknown one. The recipe:

1. Identify the relationship: vertically opposite? linear pair? corresponding? alternate?
2. Write an equation: equal-to or sum-to-180.
3. Solve for the unknown.
4. Mark it back on the diagram and sanity-check (acute should look acute, obtuse should look obtuse).

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