PLZ HELP I WANNA UNDERSTaND THIS!! (geometry)?

Question

Ok so,

In triangle DEF, the sum of the measures of angle D and angle E is 110. The sum of the measures of angle E and angle F is 150. Find the sum of the measures of angle D and angle F.

Thank you so much for your help!
I just really want to understand this
so if you could say how you did it
it would really really help!

Thanks!

Answer 1

In triangle DEF, the sum of the measures of angle D and angle E is 110. The sum of the measures of angle E and angle F is 150. Find the sum of the measures of angle D and angle F.
F = 180 - (D+E) = 70
D = 180 - (E+F) = 30
D+F = 30+70 = 100

Answer 2

Let D, E, and F be the angles of triangle DEF.

What we know is that the sum of the angles of a triangle *always* add up to 180. This tells you

D + E + F = 180


We're given that the sum of angle D and angle E is 110, so

D + E = 110

We're given that the sum of angle E and angle F is 150, so

E + F = 150

Three equations, three unknowns:

D + E + F = 180
D + E = 110
E + F = 150

There are several ways to do this; I'll present you one.

Since

D + E + F = 180, let me put D + E in brackets so I can show something to you.

(D + E) + F = 180

BUT, we're given that D + E = 110, so we can replace (D + E) entirely by 110.

110 + F = 180

Now, we calculate F as per regular algebra.
F = 70

Similarly, since

D + (E + F) = 180

and E + F = 150, then

D + 150 = 180, then
D = 30

Now we have D = 30, and F = 70.
Since we want D + F, we just add them together.

D + F = 30 + 70 = 100

Answer 3

OK since angles D and E added together give you 110 you'd subtract that from 180(that's the total measure of all the angles) and that'd give you angle F.

so F = 70.

now do 150 - 70 and get 80 so angle E = 80.

to get angle D add angels F and E then subtract from 180.

So D would equal 30.

then add D(30) to F(70) and you'll get the sum of angles D and F which is 100.

Answer 4

the sum of all three angles should measure 360

so the trick is to add up the two angle measurements you have and subtract it from 360 to know what the third angle measurement is

so 110 + 150 = 260
and 360 - 260 = 100

measurement of D and F is 100

(this would be much easier to explain if i could draw out the triangle...lol)

i hope that helped some--good luck

Answer 5

Well the sum of angles in any triange is always 180, if you know that D&E add up to 110 then you know what F is, so then you subltract F from the sum of E&F and you know what E is and you also know what D is.
Email me if you have any more problems with this.

Answer 6

that's going to be severe high quality to take the pill contained interior the morning and proceed taking mutually thereafter. tell your mom and dad the the suggestion of a medically experienced expert. If there are any doubts call the wellbeing practitioner on call.

Answer 7

Hey ' ♫ singin_gu... ♫,' you make yourself sound so grateful for help, and give all these heartfelt come-ons, but you just don't bother to read and decide "Best Answers," or resolve ties. Why should anyone bother to answer you?

Answer 8

O_O why was geometry born?