How to do this math problem? ?

Question

another math problem plz help.

In triangle DEF, the degree measure of angle D is 40 less than the degree measure of angle E, and 50 less than that of Angle F

What is the measure of D?

PLz help thx again.

Answer 1

ok

E = D + 40

F = D + 50

D + E + F = 180

D + (D + 40) + (D + 50) = 180

3D + 90 = 180

3D = 90

D = 30

E = 70

F = 80

Answer 2

Since its a triangle, D+E+F should be 180

D=E-40,  So, E=D+40

D=F-50, So, F=D+50.

Substitute in first line for E&F:

D+D+40+D+50 = 180

3D = 180-90 = 90

D=30

Answer 3

D=30

Answer 4

First write two equations for the measure of D in terms of E and F:

Equation 1:

"The degree measure of angle D is 40 less than the degree measure of angle E"

D = E - 40

Equation 2:

"...and 50 less than that of Angle F"

D = F - 50

Also remember that the sum of all the angles in a triangle is 180° so write a 3rd equation.

Equation 3:

D + E + F + 180

You now have 3 equations and 3 unknowns.

Eq 1: D = E - 40

Eq 2: D = F - 50

Eq 3: D + E + F + 180

Solve Eq. 1 for E:

E = D + 40

Solve Eq. 2 for F:

F = D + 50

Substitute these values into Eq. 3:

D + (D + 40) + (D + 50) = 180

3D + 90 = 180

3D = 90

D = 90/3

D = 30°

If you want to go further, you can plug this value back in to solve for E and F:

E = D + 40

E = 30 + 40

E = 70°

F = D + 50

F = 30 + 50

F = 80°

Answer:

D = 30°

E = 70°

F = 80°

Answer 5

the internal angle must = 180 degrees so D=30  E=70  F=80

Answer 6

D = E-40........(1)

  

D = F-50

so, F = D + 50

F = E-40 +50.......FROM (1)

F = E +10  .......(2)

D+E+F = 180

E-40 +E + E +10 = 180.............from (1) and (2)

3E -30 = 180

3E = 210

E = 70 deg

so D = E -40 = 70-40 = 30 deg

D = 30deg

Answer 7

okay basically you are given these three known equations

d is 40 less then e so-

d+40=e

d is 50 less then f so-

d+50=f

we know that all of the angles of a triangle must add to be 180 degrees so-

d+e+f=180

well lets replace the e and f with the equations we found using e instead.

so

d+(d+40)+(d+50)=180

lets combine like terms

3d+90=180

and solve

3d=90

d=30

so angle d is measured as 30 degrees.

hope that helps