An angle bisector can be defined as the line segment which divides the given angle into two equal parts. If in a triangle there will be three angle bisectors. If we draw the angle bisectors in a triangle the intersection of the angle bisectors is called as the in-center of the triangle. Using the in-centre of a triangle we can draw the in-circle of a triangle. In-centre of the triangle is represented by the letter ‘I’.For example there is an angle that is angled ABC which makes an angle at B 80 degrees. Now the line BD is dividing the given angle into two equal parts such as angle ABD is 40 degrees and angle DBC is 40 degrees. Now BD can be called as the angular bisector of angle ABC.
Following are the examples based on the concept of angle bisectors.
Example 1:Given that angle ABC is given as 140 degrees, and BD is an angle bisector to then find out the angles after the bisector is divided the angle ABC.
Solution:The given angle is ABC is 140 degrees now the angles made after the BD cuts the angle is angle ABD is 70 and DBC is 70 degrees.
Example 2:Given that the angle is PQR is 70 degrees and QS is angle bisector find out the angles.
Solution: - Given that PQR is 70 degrees now if QS cuts the angle then the angles made are PQS is 35 degrees and angle SQR is 35 degrees.