How many pairs of adjacent angles, in all, can you name in figure?

How many pairs of adjacent angles, in all, can you name in figure?

1. A
8
2. B
7
3. C
12
4. D
10

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Solution:

Given,
The pairs of adjacent angles are:
1. $\angle \mathit{AOB}$ and $\angle \mathit{BOC}$ 2. $\angle \mathit{AOB}$ and $\angle \mathit{BOD}$ 3. $\angle \mathit{AOB}$ and $\angle \mathit{BOE}$ 4. $\angle \mathit{BOC}$ and $\angle \mathit{COD}$ 5. $\angle \mathit{BOC}$ and $\angle \mathit{COE}$ 6. $\angle \mathit{COD}$ and $\angle \mathit{AOC}$ 7. $\angle \mathit{COD}$ and $\angle \mathit{DOE}$ 8. $\angle \mathit{DOE}$ and $\angle \mathit{BOD}$ 9. $\angle \mathit{DOE}$ and $\angle \mathit{AOD}$ 10. and $\angle \mathit{AOC}$ Hence there are 10 pairs of adjacent angles.
Hence, option 4 is correct.

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