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Per:Homework 4: Angle Addition Postulate** This is a 2-page document! **231. Use the diagram below to complete each part.a) Name the vertex of 24.D1b) Name the sides of 21.5 Bc) Write another name for 25.E 4d) Classify each angle:FZFBC:ZEBE:ZABC:g) Name an angle bisector.• BF I ACh) If mZEBD = 36° and mZDBC = 108°, find mZEBC.i) If mZEBF = 117°, find mZABE.2. If mZMKL = 83', mZJKL = 127", and3. If mZEFH = (5x + 1), m_HFG = 62, andmZJKM = 19% - 10)", find the value of x.mZEFG = (18x + 11), find each measure.АM15H

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MrRoyal

An angle is an undefined term in plane geometry.

  • The vertex of  [tex]\angle 4[/tex] is B
  • The sides of [tex]\angle 1[/tex] are BC and BD
  • Another name for[tex]\angle 5[/tex]  is [tex]\angle DBE[/tex]  
  • [tex]\angle FBC[/tex]is a right angle
  • [tex]\angle EBF[/tex] is an obtuse angle
  • [tex]\angle ABC[/tex] is a straight angle.
  • [tex]\angle EBC = 144[/tex]
  • [tex]\angle ABF = 13.5[/tex]

I've added as an attachment, the image of the complete question.

Vertex of [tex]\angle 4[/tex]

The vertex of an angle is the point where the rays that form the angle meet.

From the diagram, rays BE and BA meet at point B to form [tex]\angle 1[/tex].

Hence, B is the vertex

Sides of [tex]\angle 1[/tex]

The sides of an angle are the rays that form the angle

[tex]\angle 1[/tex]is formed by rays BC and BD

Hence, the sides are BC and BD

Another name for [tex]\angle 5[/tex]

An angle is named by combining the two sides and a vertex.

  • The sides of [tex]\angle 5[/tex] are DB and BE,
  • The vertex is B

This means that rays meet at point B

Hence, another name is [tex]\angle DBE[/tex]

Classify the angles

Angles are classified based on their value  

  • [tex]\angle FBC[/tex] is a right angle, because [tex]\angle FBC = 90^o[/tex]
  • [tex]\angle EBF[/tex] is an obtuse angle because [tex]\angle EBF[/tex] is greater than [tex]90^o[/tex] but less than [tex]180^o[/tex]
  • [tex]\angle ABC[/tex] is a straight angle, because [tex]\angle ABC =180^o[/tex]

Angle bisector

Ray BE is an angle bisector, because it divides [tex]\angle DBA[/tex] into two equal halves.

Find [tex]\angle EBC[/tex]

We have:

[tex]\angle EBD = 36[/tex]

[tex]\angle DBC = 108[/tex]

So:

[tex]\angle EBC = \angle EBD + \angle DBC[/tex]

[tex]\angle EBC = 36 + 108[/tex]

[tex]\angle EBC = 144[/tex]

Find [tex]\angle ABE[/tex]

We have:

[tex]\angle EBF = 117[/tex]

[tex]\angle DBC = 108[/tex]

So:

[tex]\angle EBF = \angle ABE + \angle EBD + \angle ABF[/tex]

Where

[tex]\angle ABF = 90[/tex]

[tex]\angle ABE = \angle EBD[/tex]

So:

[tex]117 = \angle ABE + \angle ABF + 90[/tex]

[tex]117 = 2\angle ABF + 90[/tex]

Subtract 90 from both sides

[tex]27 = 2\angle ABF[/tex]

Divide through by 2

[tex]\angle ABF = 13.5[/tex]

Read more about angles at:

brainly.com/question/13954458

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