Respuesta :

Answer:

[tex]m\angle EBD=40^{\circ}[/tex]

Step-by-step explanation:

We have been given a diagram. We are asked to find the measure of angle EBD.

Since ray BD is angle bisector of angle EBC, so measure of angle EBD will be equal to measure of angle DBC.

[tex]m\angle DBC=m\angle EBD[/tex]

[tex]6x+4=4x+16[/tex]

[tex]6x-4x+4=4x-4x+16[/tex]

[tex]2x+4=16[/tex]

[tex]2x+4-4=16-4[/tex]

[tex]2x=12[/tex]

[tex]\frac{2x}{2}=\frac{12}{2}[/tex]

[tex]x=6[/tex]

To find measure of angle EBD, we will substitute [tex]x=6[/tex] in expression [tex]4x+16[/tex] as:

[tex]m\angle EBD=4(6)+16[/tex]

[tex]m\angle EBD=24+16[/tex]

[tex]m\angle EBD=40[/tex]

Therefore, measure of angle EBD is 40 degrees.

abidemiokin

the measure of m<EBD is 40degrees

The point where two lines meet is known as the angle.

From the given diagram, we are told that BD bisects,<EBC, this means that BD divides <EBC into two equal parts. Therefore:

  • m<EBD = m<DBC

4x+16 = 6x+4

4x-6x = 4 - 16

-2x = -12

x = 12/2

x = 6

Next is to get the measure of m<EBD

m<EBD = 4x+16

m<EBD = 4(6) + 16

m<EBD = 24 + 16

m<EBD = 40

Hence the measure of m<EBD is 40degrees

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