Question

"Question 1 In the given figure, lines AB and CD intersect at O. If and find ∠BOE and reflex ∠COE.

Class 9 - Math - Lines and Angles Page 96"

Answer 1

Reflex angle:

An angle whose measure is more than 180° but less than 360° is called a reflex angle

 

Linear pair of angles:

If Non common arms of two adjacent angles form a line, then these angles are called linear pair of angles.

 

Vertically opposite angles:

When two line intersect each other at a point then there are two pairs of vertically opposite angles.

 

Axiom- 1

If a ray stands on a line, then the sum of two adjacent angles so formed is 180°i.e, the sum of the linear pair is 180°.

 THEOREM 1:

If two lines intersect each other then the vertically opposite angles are equal.

 

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Solution:

The linear pair axiom and theorem 1 are used to solve this question.

 

Given,

∠AOC+∠BOE = 70°....(1)

 & ∠BOD = 40°.....(2)

Also Lines AB & CD intersect each other at O.

∠AOC= ∠BOD

 [vertically opposite angles]

∠AOC=40°

From eq question 1

 

∠AOC+∠BOE = 70°

40°+∠BOE = 70°

∠BOE = 70°-40°=30°

 

∠AOC+∠BOC = 180°

[By linear pair axiom]

 

∠BOC= ∠BOE +∠COE

 

∠AOC + (∠BOE +∠COE) = 180

From eq 1

⇒ 40° +∠COE+30° = 180°

⇒ 70°+∠COE = 180°

 

∠COE = 180°-70°=110°

∠COE+ reflex∠COE= 360°

 

[Since sum of angles at a point is 360°]

 

Reflex ∠COE= 360-110°=250°

 

Hence, ∠BOE= 30° & reflex ∠COE= 250°

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Hope this will help you....

Answer 2

Reflex of angle COE= 360-110=250