M∠abc=95° find m∠abd and m∠dbc. explain how to do this

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.

Learn more here: link

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° .

Substitute value of each angle in the above equation.

Comparing the measure we get

On combining like terms we get

Subtract 18 from both sides.

Divide both sides by 11.

The value of x is 7.

Therefore m∠ABD=37° and m∠DBC = 58°.

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584