Question

If all the lines of the given figure are straight lines, then what is the value of a + b +c+d+e+f=?​

Answer 1

Answer:

Correct option is

A

360

∘

Here, AOB,COD,EOF are triangles.

Then by angle sum property,

∠a+∠b+∠AOB=180

o

...(i),

∠c+∠d+∠COD=180

o

...(ii)

and ∠e+∠f+∠EOF=180

o

...(iii).

Also, AOB,COD and EOF are straight lines.

Then, ∠EOF=∠BOC ...[Vertically opposite angles].

So, ∠AOB+∠COD+∠BOC(=∠EOF)=180

o

...(iv) ...[Straight line].

Then, (i),(ii) and (iii),

∠a+∠b+∠AOB+∠c+∠d+∠COD+∠e+∠f+∠EOF=180

o

×3=540

o

⟹ ∠a+∠b+∠c+∠d+∠e+∠f+∠AOB+∠COD+∠EOF=540

o

....[Substitute (iv)]

⟹ ∠a+∠b+∠c+∠d+∠e+∠f+180

o

=540

o

⟹ ∠a+∠b+∠c+∠d+∠e+∠f=360

o

.

Therefore, option A is correct.

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