Question

ABC is a triangle in which angle A equal to 66°, the internal bisectors of Angle B and angle C intersect at O. Find the measurement of angle BOC. ​

Answer 1

Answer:

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Answer 2

Answer:

The answer to the given question is 123°

Step-by-step explanation:

Given:

ABC is a triangle

angle A is equal to 66°.

The internal directors of angle B and angle C intersect at O.

To find :

Measurement of angle BOC.

Solution :

As we know that the sum of the angles of the triangle is equal to 180°.

let's calculate that

66°+ angle B +angle C=180°

angle B + angle C = 180°-66°.

angle B+ angle C = 114°.

Divide each term by 2.

$\frac{1}{2} b + \frac{1}{2} c = \frac{114}{2} = 57$

Therefore angle 1 + angle 2 = 57°.

BO and CO are sectors of angle B and angle C respectively.

In triangle BOC , we have

angle 1 + angle 2+ <BOC =180°.

57°+<BOC=180°.

As the sum of angles of the triangle is always equal to the 180°.

angle <BOC= 180°-57°

The angle <BOC = 123°.

Therefore, the final answer to the given question is 123°.

The measurement of angle BOC is 123°.

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