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Shtirlitz [24]
2 years ago
14

Ray BD bisects angle ABC. Ray BE bisects angle ABD, and Ray BF bisects angle EBD. If angle ABE = 20 degrees, find the measure of

angle FBC. (in degrees)
Mathematics
1 answer:
Mars2501 [29]2 years ago
8 0

An <em>angle bisector</em> is a <u>straight line</u> that <em>divides</em> a given <u>angle</u> into two <u>equal</u> measures. Thus the measure of <u>angle</u> FBC is 50^{o}.

A <u>line</u> that <em>divides</em> a given measure of angle into <em>two equal</em> measures is referred to as an <em>angle bisector</em>. This makes the <em>two angles</em> produced by the <u>bisector</u> to be <u>congruent</u>.

Thus from the given question, we have;

<ABD + <DBC = < ABC (<u>addition</u> property of a <em>bisected angle</em>)

<ABE + <EBD = <ABD (<u>addition</u> property of a bisected angle)

<EBF + <FBD = <EBD (<u>addition</u> property of a <em>bisected angle</em>)

Given that angle ABE = 20^{o}, thus;

<ABE = <EBD = 20^{o}

Then,

<EBF + <FBD =    20^{o}

<EBF = <FBD = 10^{o}

Such that;

<FBC = <FBD + <DBC

         = 10^{o} + 2<ABE

         =  10^{o} + 40^{o}

<FBC = 50^{o}

Therefore, the <em>measure</em> of <u>angle</u> FBC is 50^{o}.

For more clarifications on bisection of a given angle, visit: brainly.com/question/17247176

#SPJ1

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