An angle bisector is a line segment that divides an angle into two
The measure of angle ∠ABC is 50° (degrees)
The reason for arriving at the above angle measurement is s follows:
The given information are;
The segment BD = The angle bisector of the angle ∠ABC
∠ABD = 5·x
∠DBC = 3·x + 10
Method:
Calculate the vale of x based on the given angular relationships
Solution:
By angle addition postulate, we have;
∠ABD + ∠DBC = ∠ABC
Given that BD bisects angle ∠ABC, (into two equal angles), to give ∠ABD and ∠DBC, we get;
∠ABD = ∠DBC
By substitution property, we get;
5·x = 3·x + 10
Which gives;
5·x - 3·x = 10
2·x = 10
x = 10/2 = 5
x = 5
Therefore, from ∠ABD + ∠DBC = ∠ABC, where, ∠ABD = 5·x, and ∠DBC = 3·x + 10, we get;
∠ABD + ∠DBC = 5·x + 3·x + 10 = 8·x + 10 = ∠ABC
∠ABC = 8·x + 10
Plugging in the value of x into the above equation gives;
∠ABC = 8 × 5 + 10 = 50
Angle ∠ABC = 50°
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