In the given figure, two straight lines AB and CD intersect at a point O. If ∠BOD = 40°, find the measure of each of the angles, ∠BOC, ∠AOC and ∠AOD.
Lines & Angles
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Question

In the given figure, two straight lines AB and CD intersect at a point O. If ∠BOD = 40°, find the measure of each of the angles, ∠BOC, ∠AOC and ∠AOD.

KnowledgeBoat · Accepted Answer

Given: ∠BOD = 40° When two lines intersect, the angles opposite to each other are equal. ∠AOC = ∠BOD [Vertically opposite angles] ∴ ∠AOC = 40° Since AOB is a straight line, ∠BOC and ∠BOD form a linear pair and must sum to 180° ∠BOC + ∠BOD = 180° Substituting the value of ∠BOD in above, we get: ⇒ ∠BOC + 40° = 180° ⇒ ∠BOC = 180° - 40° ⇒ ∠BOC = 140° ∠AOD = ∠BOC [Vertically opposite angles] ∴ ∠AOD = 140° ∠AOC = 40°, ∠BOC = 140° and ∠AOD = 140°.

Mathematics

In the given figure, two straight lines AB and CD intersect at a point O. If ∠BOD = 40°, find the measure of each of the angles, ∠BOC, ∠AOC and ∠AOD.

Lines & Angles

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