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Line segments AB and CD intersect at O such that $A C ‖ D B$ .If $∠ C A B = 45 °$ and $∠ C D B = 55 °$ , then the measure of $∠ B O D$ is ____°.

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Detailed Solution

Line segments AB and CD intersect at O such that

A C ‖ D B

.If

∠ C A B = 45 °

and

∠ C D B = 55 °

, then the measure of

∠ B O D

is 80°.
Given a figure in which line segments AB and CD intersect at O such that

A C ‖ D B

and

∠ C A B = 45 °

∠ C D B = 55 °

Line segments AB and CD inersect at O such that AC | |DB. If ∠ CAB =45∘ and ∠ CDB=55∘, then ∠ BOD=

As we know that, alternate interior angles are equal.
Therefore,

∠ O B D = ∠ C A B ⇒ ∠ O B D = 45 °

Using angle sum property in triangle ODB,

∠ O B D + ∠ O D B + ∠ B O D = 180 ° ⇒ 55 ° + 45 ° ∠ B O D = 180 ° ⇒ ∠ B O D + 100 ° = 180 ° ⇒ ∠ B O D = 180 ° − 100 ° ⇒ ∠ B O D = 80 °

Hence, the measure of

∠ B O D

is 80°.

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