Question

SOMEONE PLEASE HELP ME

Answer 1

m∠BFC = 73°

Step-by-step explanation:

Given the angles and bisectors in the figure, you want the measure of angle BFC.

Angles

AC bisects angle BAD, so angle BAC is the same as angle CAD, 30°.

The sum of angles BAD and ADB is 60° +34° = 94°, so the measure of angle ABD is ...

∠ABD = 180° -94° = 86°

BE bisects angle ABD, so the measure of angle ABE is 86°/2 = 43°.

Exterior angle

An exterior angle of a triangle is equal to the sum of the remote interior angles.

The angle of interest, ∠BFC, is an exterior angle to triangle AFB, so is the sum of angles FAB and FBA.

∠BFC = 30° +43°

∠BFC = 73°

Answer 2

Answer: 73 degrees

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Step-by-step explanation:

We're given that segment AC bisects angle BAD.

This means the angle has been split into two equal parts.

Angle CAD = angle BAC = 30

So,

angle BAD = (angleCAD)+(angleBAC) = 30+30 = 60 degrees

Let's find angle ABD. I'll use the fact that the three interior angles of a triangle always add to 180. This idea will be used a few times in this solution.

(angeBDA)+(angleBAD)+(angleABD) = 180

(34)+(60)+(angleABD) = 180

94+angleABD = 180

angleABD = 180-94

angleABD = 86

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We're also given that segment BE bisects angle ABD, which means:

angleABE = angleEBD = 86/2 = 43

We'll use angle ABE and angle BAD to determine angle AEB.

(angeABE)+(angleBAD)+(angleAEB) = 180

(43)+(60)+(angleAEB) = 180

103+(angleAEB) = 180

angleAEB = 180-103

angleAEB = 77

This is the same as angle AEF.

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Now focus your attention on triangle EFA.

(angeAEF)+(angleFAE)+(angleEFA) = 180

(77)+(30)+(angleEFA) = 180

107+(angleEFA) = 180

angleEFA = 180-107

angleEFA = 73

Notice how angle EFA and angle BFC are vertical angles. Therefore, they are congruent and we can say angle BFC = 73