Question

The sum of all angles in a triangle is always 180 degrees. The measure of the first angle is four times the measure of the second angle. The measure of the third angle is 78° more than the second angle. What is each angle?

Answer 1

Ready to work on this together?

Answer 2

aw yeah big answer time!

Answer 3

Awww yeah! Lol.
Boog! Still here? We're going to solve this together, but I need your input.

Answer 4

ok

Answer 5

Awesome. First things first, how many degrees will the total equal? As in, if we have:
side one + side two + side three = ?????, what is ?????

Answer 6

i am assuming 180

Answer 7

That's right!

So we have:
blahblahblah = 180

So far so good?

Answer 8

yes

Answer 9

Awesome. Now let me rewrite the question so we don't have to keep scrolling.

Answer 10

ok

Answer 11

The sum of all angles in a triangle is always 180 degrees. The measure of the first angle is four times the measure of the second angle. The measure of the third angle is 78° more than the second angle. What is each angle?

Answer 12

Ok. So we see that angle one and angle three are using angle two as our reference point, right?

Answer 13

yes

Answer 14

By reference, I mean they're comparing the two angles to the second angle. Does that part make sense?

Answer 15

i think so

Answer 16

Do we know exactly how big angle 2 is right now?

Answer 17

no

Answer 18

Good. So how do we translate this: "The measure of the first angle is four times the measure of the second angle." to math language?

Answer 19

In other words, angle 1 = "what"?

Answer 20

thats where i get lost

Answer 21

Ok, not a problem.

Answer 22

Think of it this way: If I said "bob is 100 feet tall, and jill is twice as tall", how would you write that as an equation?

Answer 23

x=100*2

Answer 24

good!
So here's our problem: In our question, we don't know how big angle 2 is. So how do we say "four times bigger than an unknown angle"?

Answer 25

Or, more directly, how do we say "four times an unknown"?

Answer 26

x=4*x?

Answer 27

Well, y = 4x
Where y is angle 1, and x is angle 2.

Answer 28

ok

Answer 29

Otherwise, we'd be saying "X is four times bigger than X" which wouldn't really work. ;)

Answer 30

i see that now

Answer 31

Alright. So here's what we know so far:
Angle one is equal to 4x
And angle two is equal to just x.

Answer 32

The sum of all angles in a triangle is always 180 degrees. The measure of the first angle is four times the measure of the second angle. The measure of the third angle is 78° more than the second angle. What is each angle?

Answer 33

Show me how we represent angle 3 now.

Answer 34

And don't let the degree sign throw you off. Just treat it as a 78

Answer 35

i have no clue

Answer 36

Well, how do they describe angle three to us? Tell me what they say.

Answer 37

The measure of the third angle is 78° more than the second angle.

Answer 38

x=3*78?

Answer 39

Close. Remember it's saying it's exactly 78 degrees more. Not 78 *times* bigger.

Answer 40

also, the three is not needed. Even though it's the third angle, we don't use the three for the mathematical expression.

Answer 41

The measure of the third angle is 78° more than the second angle.

Answer 42

what was the second ?

Answer 43

Remember this part:
"Alright. So here's what we know so far:
Angle one is equal to 4x
And angle two is equal to just x."

Answer 44

x+78?

Answer 45

i have never had algebra before, so word problems are hard for me to understand

Answer 46

Perfect! You're absolutely right.

Answer 47

Oh dear. They should have had you take algebra before you took geometry.

Answer 48

Or is this algebra class right now?

Answer 49

collage math 101

Answer 50

so 4x+78?

Answer 51

Ah. That is actually algebra 1 then. :D

Here we go:
you know that:
angle 1 is 4x
angle 2 is x
angle 3 is x+78

Answer 52

Not yet, I'm afraid. We know from earlier that we said:

angle 1 plus angle 2 plus angle 3 = 180 right?

Answer 53

right

Answer 54

so 180 needs to go some where

Answer 55

if i can figure out the equation i can get the answer

Answer 56

4x+x+78=180?

Answer 57

Perfect! Do you know about combing like terms and everything else?

Answer 58

Oh wait!
We forgot ONE thing.

Answer 59

4x = angle 1
x+78 is angle 3
and x is angle 2

Do you see what you're missing?

Answer 60

ok

Answer 61

Hint: putting the expressions in parentheses makes it more obvious:

(4x) + (x+78) =180

So what are we missing?

Answer 62

4x+x+78*2?

Answer 63

the two didn't come from any of our equations.

Answer 64

sorry read it wrong

Answer 65

Hint:
(4x) + (x+78) =180 <-- total angles
^ Angle 1 ^ angle 3

Answer 66

No problem. So you see what's missing, right?

Answer 67

angle 2

Answer 68

Perfect!

Answer 69

now i am lost again

Answer 70

So we just sneak in an extra +x, right?

Answer 71

4x + x+78 + x =180

Answer 72

(4x)+(x+78)+x=180

Answer 73

Perfect! Now combine like terms.

Answer 74

(you can now drop the parentheses if you want)

Answer 75

78 + 4x + x + x = 180

Answer 76

4x + x = 5x

Answer 77

78 + 5x + x = 180

Answer 78

Good! And keep going.

Answer 79

5x + x = 6x

Answer 80

78 + 6x = 180

Answer 81

Excellent! Now what do we do?

Answer 82

78 + -78 + 6x = 180 + -78

Answer 83

Absolutely right.

Answer 84

6x = 180 + -78

Answer 85

yep. So 6x = 102

Answer 86

180 + -78 = 102

Answer 87

And x equals how much?

Answer 88

17

Answer 89

so 17 is 1 answer?

Answer 90

Exactly! Which angle did we decide was 17? As in, what angle did we decide would be "x"?

Answer 91

2

Answer 92

Perfect! You now have all the information needed to solve.

Answer 93

The sum of all angles in a triangle is always 180 degrees. The measure of the first angle is four times the measure of the second angle. The measure of the third angle is 78° more than the second angle. What is each angle?

Answer 94

(4x)+x+78)+17=180?

Answer 95

well, we only needed that equation to find what x equals. We know that
4*17 + 17+78 + 17 = 180

Answer 96

Oh crap nevermind that.. i read the question wrong

Answer 97

Woogy: Tell me mathematically how you got that.

Answer 98

Oh ok. Mistakes happen. ^_^