Refer the figure and identify which of the following are correct?

∠ A O D = 138 °

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∠ A O D = 42 °

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∠ B O D = 42 °

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∠ B O D = 138 °

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Solution

The correct options are
A $∠ A O D = 138 °$
C $∠ B O D = 42 °$

$Given, ∠ C O A = 42 ° .$

$∠ A O D + ∠ C O A = 180 ° (Linear Pair) ∠ A O D + 42 ° = 180 ° ∠ A O D = 180 ° - 42 ° = 138 ° Hence, ∠ A O D = 138 ° .$

$∠ C O A = ∠ B O D = 42 ° (Vertically Opposite angles)$

$Thus, ∠ A O D = 138 ° and ∠ B O D = 42 ° .$

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