In the given figure, two lines AB and CD intersect at a point O. If ∠AOC + ∠BOD = 70°, find the measure of ∠AOD.
Lines & Angles
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Question

In the given figure, two lines AB and CD intersect at a point O. If ∠AOC + ∠BOD = 70°, find the measure of ∠AOD.

KnowledgeBoat · Accepted Answer

In the given figure, two straight lines AB and CD intersect at point O. When two lines intersect, the angles opposite to each other are equal: ∴ ∠AOC = ∠BOD [Vertically opposite angles] The question states that: ∠AOC + ∠BOD = 70° Since they are equal, we can replace ∠BOD with ∠AOC in the equation: ⇒ ∠AOC + ∠AOC = 70° ⇒ 2∠AOC = 70° ⇒ ∠AOC = ⇒ ∠AOC = 35° So, ∠AOC = 35° and ∠BOD = 35°. Since CD is a straight line, the angles ∠AOC and ∠AOD form a linear pair and must sum to 180°. ∴ ∠AOC + ∠AOD = 180° ⇒ 35° + ∠AOD = 180° ⇒ ∠AOD = 180° - 35° ⇒ ∠AOD = 145° The measure of ∠AOD is 145°.

Mathematics

In the given figure, two lines AB and CD intersect at a point O. If ∠AOC + ∠BOD = 70°, find the measure of ∠AOD.

Lines & Angles

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