Question

In figure, three coplanar lines AB, CD and EF interest at a
point O. Find the value of x . Hence, find ∠AOD, ∠COB

Answer 1

Answer:

Here's your answer buddy!

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Step-by-step explanation:

∠DOF = ∠COE (Vertically opposite angles)

Therefore ∠DOF = ∠COE = 5x°

∠AOF + ∠DOF + ∠BOD = 180° (Adjacent angles lying on a straight line)

or, 2x + 5x + 3x = 180°

or, 10x = 180°

or, x = 18°

Therefore value of x is 18°.

Hence,

∠AOF = 2×18° = 36°

∠DOF = ∠COE = 5×18° = 90°

∠BOD = 3×18° = 54°

Now,

∠AOD = ∠AOF + DOF

or, ∠AOD = 36° + 90°

or, ∠AOD = 126°

⇒ ∠AOD = 126°

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Now,

∠COE + ∠BOE + ∠BOD = 180° (Adjacent angles lying on a straight line)

or, 90° + ∠BOE + 54° = 180°

or, ∠BOE + 144° = 180°

or, ∠BOE = 180° - 144°

or, ∠BOE = 36°

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∠COB = ∠COE + ∠BOE

or, ∠COB = 90° + 36°

or, ∠COB = 126°

⇒ ∠COB = 126°

Notes:-

Since ∠COB = ∠AOD, it also tells are that they are vertically opposite angles, and that points DOC and AOB lie on the same straight line.

In other words, we can also use the theory of vertically opposite angles, to find ∠COB, which is equal to ∠AOD that is 126°.

What are vertically opposite angles?

Vertical angles are a pair of opposite angles formed by intersecting lines.

What is the theory of vertically opposite angles?

Vertical opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.

For example, in your question, CD and FE are two lines intersecting with each other, thereby forming two pairs of vertically opposite angles. In this case, ∠DEF = ∠COE and ∠DOE = COF.

Hope you'll understand it.

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