Which of the following equal(s) $∠ A O B$ ?

$∠ A O D + ∠ D O C + ∠ C O B$

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$∠ A O D + ∠ C O B$

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$∠ A O C + ∠ C O B$

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$∠ A O D + ∠ D O B$

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Solution

The correct options are
A
$∠ A O D + ∠ D O C + ∠ C O B$

C
$∠ A O C + ∠ C O B$

D
$∠ A O D + ∠ D O B$

Note that $∠ A O B$ can be obtained in the following different ways:
$∠ A O D + ∠ D O B$ ,
$∠ A O C + ∠ C O B$ and
$∠ A O D + ∠ D O C + ∠ C O B$ .
Also note that $∠ A O D + ∠ C O B$ does not equal $∠ A O B$ . In fact, $∠ A O D + ∠ C O B$ = $∠ A O B - ∠ D O C$ since
$∠ A O D + ∠ D O C + ∠ C O B = ∠ A O B$ .

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Which of the following equal(s) ∠AOB?

Which of the following equal(s) $∠ A O B$ ?