An angle bisector is a straight line that divides a given angle into two equal measures. Thus the measure of angle FBC is [tex]50^{o}[/tex].
A line that divides a given measure of angle into two equal measures is referred to as an angle bisector. This makes the two angles produced by the bisector to be congruent.
Thus from the given question, we have;
<ABD + <DBC = < ABC (addition property of a bisected angle)
<ABE + <EBD = <ABD (addition property of a bisected angle)
<EBF + <FBD = <EBD (addition property of a bisected angle)
Given that angle ABE = [tex]20^{o}[/tex], thus;
<ABE = <EBD = [tex]20^{o}[/tex]
Then,
<EBF + <FBD = [tex]20^{o}[/tex]
<EBF = <FBD = [tex]10^{o}[/tex]
Such that;
<FBC = <FBD + <DBC
= [tex]10^{o}[/tex] + 2<ABE
= [tex]10^{o}[/tex] + [tex]40^{o}[/tex]
<FBC = [tex]50^{o}[/tex]
Therefore, the measure of angle FBC is [tex]50^{o}[/tex].
For more clarifications on bisection of a given angle, visit: https://brainly.com/question/17247176
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