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In the given isosceles triangle, if the bisectors of $∠ B$ and $∠ C$ meet at a point O and $∠ A = 40 °,$ then what will be the value of $∠ B O C$ ?

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110 °

70 °

130 °

150 °

answer is A.

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Detailed Solution

It is given that the bisectors of

∠ B

and

∠ C

meet at a point O and

∠ A = 40 ° .

It means that

∠ B = ∠ C .

We know that the total sum of all the angles in a triangle is equal to

180 ° .

So in

Δ A B C,

we have,

∠ A + ∠ B + ∠ C = 180 ° ⇒ 40 ° + ∠ B + ∠ B = 180 ° ∵ ∠ A = 40 °, ∠ B = ∠ C ⇒ 2 ∠ B = 140 ° ⇒ ∠ B = 70 °

Since we know the bisector divides an angle into equal parts, therefore,

∠ O B C = 35 ° and ∠ O C B = 35 °

Using this in

Δ O B C,

we will get,

∠ B O C + ∠ O B C + ∠ O C B = 180 ° ⇒ ∠ B O C + 35 ° + 35 ° = 180 ° ⇒ ∠ B O C + 70 ° = 180 ° ⇒ ∠ B O C = 110 °

Therefore, the value of

∠ B O C = 110 ° .

Thus, option (1) is correct.

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