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In the adjoining figure, the three lines AB, CD and EF all pass through the point O. If ∠EOB = 90° and x:y = 2:1 then ∠BOD and ∠COE:-
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In the adjoining figure, the three lines AB, CD and EF all pass throug...
Given:
- AB, CD, and EF are three lines passing through the point O.
- ∠EOB = 90°
- x:y = 2:1
To find:
- ∠BOD and ∠COE
Solution:
Step 1: Understand the given information
- We have a figure with three lines (AB, CD, and EF) passing through a point O.
- The angle ∠EOB is given as 90°, which means it is a right angle.
Step 2: Analyze the lines AB, CD, and EF
- Since AB, CD, and EF all pass through the point O, we can say that they intersect at O.
- Let's analyze the lines AB, CD, and EF separately.
Line AB:
- Let's assume that the point where AB intersects the line CD is P.
- Since AB and CD intersect at P, we can say that ∠BOP and ∠POD are supplementary angles.
- Let's assume that ∠BOP = 2x and ∠POD = x.
- Since ∠BOP and ∠POD are supplementary, we can write the equation: ∠BOP + ∠POD = 180°.
- Substituting the values of ∠BOP and ∠POD, we get: 2x + x = 180°.
- Simplifying the equation, we find: 3x = 180°.
- Dividing both sides by 3, we get: x = 60°.
- Therefore, ∠BOP = 2x = 2 * 60° = 120° and ∠POD = x = 60°.
Line CD:
- Since AB and CD intersect at P, we can say that ∠POD and ∠COE are supplementary angles.
- Let's assume that ∠POD = x = 60° and ∠COE = y.
- Since ∠POD and ∠COE are supplementary, we can write the equation: ∠POD + ∠COE = 180°.
- Substituting the values of ∠POD and ∠COE, we get: 60° + y = 180°.
- Simplifying the equation, we find: y = 180° - 60° = 120°.
- Therefore, ∠COE = y = 120°.
Step 3: Final answer
- ∠BOD = ∠POD = x = 60°.
- ∠COE = y = 120°.
- AB, CD, and EF are three lines passing through the point O.
- ∠EOB = 90°
- x:y = 2:1
To find:
- ∠BOD and ∠COE
Solution:
Step 1: Understand the given information
- We have a figure with three lines (AB, CD, and EF) passing through a point O.
- The angle ∠EOB is given as 90°, which means it is a right angle.
Step 2: Analyze the lines AB, CD, and EF
- Since AB, CD, and EF all pass through the point O, we can say that they intersect at O.
- Let's analyze the lines AB, CD, and EF separately.
Line AB:
- Let's assume that the point where AB intersects the line CD is P.
- Since AB and CD intersect at P, we can say that ∠BOP and ∠POD are supplementary angles.
- Let's assume that ∠BOP = 2x and ∠POD = x.
- Since ∠BOP and ∠POD are supplementary, we can write the equation: ∠BOP + ∠POD = 180°.
- Substituting the values of ∠BOP and ∠POD, we get: 2x + x = 180°.
- Simplifying the equation, we find: 3x = 180°.
- Dividing both sides by 3, we get: x = 60°.
- Therefore, ∠BOP = 2x = 2 * 60° = 120° and ∠POD = x = 60°.
Line CD:
- Since AB and CD intersect at P, we can say that ∠POD and ∠COE are supplementary angles.
- Let's assume that ∠POD = x = 60° and ∠COE = y.
- Since ∠POD and ∠COE are supplementary, we can write the equation: ∠POD + ∠COE = 180°.
- Substituting the values of ∠POD and ∠COE, we get: 60° + y = 180°.
- Simplifying the equation, we find: y = 180° - 60° = 120°.
- Therefore, ∠COE = y = 120°.
Step 3: Final answer
- ∠BOD = ∠POD = x = 60°.
- ∠COE = y = 120°.
Community Answer
In the adjoining figure, the three lines AB, CD and EF all pass throug...
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