Respuesta :

Answer:

m∠ABD=37° and m∠DBC = 58°.

Step-by-step explanation:

Given information: m∠ABC=95°

From the given figure it is clear that m∠ABD=(2x+23)° and m∠DBC=9x-5° .

[tex]m\angle ABC=m\angle ABD+m\angle DBC[/tex]

Substitute value of each angle in the above equation.

[tex](95)^{\circ}=(2x+23)^{\circ}+(9x-5)^{\circ}[/tex]

Comparing the measure we get

[tex](95)=(2x+23)+(9x-5)[/tex]

On combining like terms we get

[tex]95=(2x+9x)+(23-5)[/tex]

[tex]95=11x+18[/tex]

Subtract 18 from both sides.

[tex]95-18=11x[/tex]

[tex]77=11x[/tex]

Divide both sides by 11.

[tex]7=x[/tex]

The value of x is 7.

[tex]m\angle ABD=(2x+23)^{\circ}=(2(7)+23)^{\circ}=37^{\circ}[/tex]

[tex]m\angle DBC=(9x-5)^{\circ}=(9(7)-5)^{\circ}=58^{\circ}[/tex]

Therefore m∠ABD=37° and m∠DBC = 58°.

abidemiokin

The measure of m∠ABD and m∠DBC are 37 and 58degrees respectively

given that m<ABC is 95degrees

The line that bisects an angle divides the angle equally and an angle is formed from the intersection of two lines.

From the given diagram:

<ABC = <ABD + <DBC

Given te following

<ABC = 95degrees

<ABD = 2x + 23

<DBC = 9x - 5

Substitute into the equation

95 = 2x + 23 + 9x - 5

95 =11x +18

11x = 95 - 18

11x = 77

x = 77/11

x =  7

Get the angle <ABD

<ABD = 2x + 23

<ABD = 2(7) + 23

<ABD = 14 + 23

<ABD = 37degrees

Get the angle DBC

<DBC = 95 - <ABD

<DBC = 95 - 37

<DBC = 58degrees

Hence the measure of m∠ABD and m∠DBC are 37 and 58degrees respectively.

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