External Bisectors of a Triangle

To find the measure of angle BOC, we need to understand the concept of external bisectors in a triangle. Given a triangle ABC, Bo and Co are the external bisectors of angles B and C, respectively. These external bisectors intersect at point O.

Step 1: Determine the measures of angles BOC and BCO

Since Bo is the external bisector of angle B, it divides angle ABC into two equal parts. Let's label the point where Bo intersects BC as D. Therefore, angle BOD is 60 degrees, as it is half of angle ABC, which is 120 degrees.

Similarly, Co is the external bisector of angle C, so it divides angle ACB into two equal parts. Let's label the point where Co intersects AB as E. Thus, angle COE is 60 degrees, as it is half of angle ACB, which is 120 degrees.

Step 2: Determine the measure of angle BOC

To find the measure of angle BOC, we need to consider angles BOD and COE. Since triangle BOD and triangle COE are both isosceles triangles (with two sides of equal length), the base angles are equal.

Therefore, angle BDO is also 60 degrees, as it is equal to angle BOD. Similarly, angle CEO is 60 degrees, as it is equal to angle COE.

Step 3: Calculate angle BOC

Angle BOC is formed by angles BDO and CEO. Since angle BDO and angle CEO are both 60 degrees, we can find the measure of angle BOC by adding these angles:

BOC = BDO + CEO = 60 degrees + 60 degrees = 120 degrees

Therefore, the measure of angle BOC is 120 degrees.

Summary:

Given that Bo and Co are the external bisectors of angles B and C, respectively, in triangle ABC, we can determine the measure of angle BOC. By dividing angles ABC and ACB into equal parts, we find that angles BOD and COE are 60 degrees each. Since triangle BOD and triangle COE are both isosceles triangles, angles BDO and CEO are also 60 degrees each. Thus, the sum of these angles, angle BOC, is equal to 120 degrees.

Ur ques is ntt correct....i mean tell the wch angle is 60