In the given figure, the lines AB, CD and EF intersect at a point O. If ∠BOD = x°, ∠AOE = 2x° and ∠COF = 90°, find ∠AOE and ∠AOC.
Lines & Angles
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Question

In the given figure, the lines AB, CD and EF intersect at a point O. If ∠BOD = x°, ∠AOE = 2x° and ∠COF = 90°, find ∠AOE and ∠AOC.

KnowledgeBoat · Accepted Answer

Given: ∠BOD = x°, ∠AOE = 2x°, ∠COF = 90° In the figure, three straight lines (AB, CD, and EF) intersect at point O. Therefore, vertically opposite angles are: ∠BOD = ∠AOC. Therefore, ∠AOC = x° ∠AOE = ∠BOF. Therefore, ∠BOF = 2x° ∠COF = ∠DOE. Therefore, ∠DOE = 90° Since AB is a straight line, the angles ∠AOE, ∠EOD and ∠DOB lie on a straight line and their sum is 180°. ∴ ∠BOD + ∠DOE + ∠AOE = 180° Substituting in the above equation, we get: x°+ 90° + 2x = 180° ⇒ 3x° + 90° = 180° ⇒ 3x° = 180° - 90° ⇒ 3x° = 90° ⇒ x° = ⇒ x° = 30° Let's find ∠AOE and ∠AOC by substituting the value of x: ∠AOE = 2x° = (2 x 30)° = 60° ∠AOC = x° = 30° ∠AOE = 60° and ∠AOC = 30°.

Mathematics

In the given figure, the lines AB, CD and EF intersect at a point O. If ∠BOD = x°, ∠AOE = 2x° and ∠COF = 90°, find ∠AOE and ∠AOC.

Lines & Angles

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