Answer :
The value of x is 4 and the value of ∠ABC is 68°.
To solve this problem we first have to understand the concept of an angle bisector. Angle bisector is a straight line passes through the vertex of an angle dividing the angle in two equal angles.
According to the condition BD bisects ∠ABC
Therefore the two angles formed by the angle bisector are ∠ABD and ∠CBD.
The angle value of these two angles are equal.
Given:
m∠ABD=11x-10
m∠CBD=8x+2
Therefore from the above condition:
m∠ABD=m∠CBD
Substituting the values we get:
11x-10=8x+2
Solving the linear equation to find the value of x.
[tex]or,11x-10=8x+2\\or,11x-8x=2+10\\or,3x=12\\or,x=4[/tex]
Now let us find the value of ∠ABC
m∠ABC=m∠ABD+m∠CBD
or,∠ABC=11x-10+8x+2
or,∠ABC=19x-8
Substituting the value x=4 in the equation we get:
m∠ABC=19×4-8
or,m∠ABC=68°
Therefore we can conclude that the value of xis 4 and the value of ∠ABC is 68°.
To learn more about angle bisectors:
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