putting this in a equation?

Question

The measure of the second angle of a triangle is three times the measure of the first angle. the measure of the third angle is 12 degrees less than twice the measure of the first. Find the measure of each of the three angles.

Answer 1

Remember, the angles of a triangle always add up to 180 degrees.

Let x = the first angle.
Second angle =3x.
Third angle = 2x - 12

So,
x + 3x + 2x - 12 = 180
6x - 12 = 180
6x = 192
x = 192/6 = 32

First angle = 32 degrees
Second angle = 96 degrees
Third angle = 52 degrees
32 + 96 + 52 = 180

Answer 2

Draw a picture to illustrate this, then assign a variable to each.


B ------ C
....\.....|
.....\....|
.......\..|
........V
........A

The measure of the second angle of a triangle [Let call it B] is three times the measure of the first angle [lets call it A]. the measure of the third angle [lets call it C] is 12 degrees less than twice the measure of the first[A]. Find the measure of each of the three angles

SO... use the variables to restate this problem:
The measure of the second angle of a triangle [Let call it B] is three times the measure of the first angle [lets call it A].
B = 3 A or A= B/3 [Equation 1]

the measure of the third angle [lets call it C] is 12 degrees less than twice[2 times] the measure of the first[ which we called A]
C = 2A - 12 or [Equation 2]

Now there is a third equation needed which is not stated in the description. Why? Because if we have three variables, we need three equations to solve. But what is it? ....well we know that the sum of all angles of a triangle is 180 degrees. Therefore:
A+B+C = 180 [Equation 3]


So, now we solve by substituting one equation into another. Start with equation 1 and equation 2 into equation 3:
A + (3A) + (2A-12) = 180
A + 3A + 2A -12 = 180 [Commutative]
6A -12 (+12) =180 (+ 12) [Add 12 to each side]
6A = 192
6A/6 = 192/6 [divide both sides by 6]
A = 32

Substitute into equation 1
B=3 (32)
B=96

Substitute A into equation 2
C = 2(32) - 12
C= 64-12 = 52

Check in equation 3
32+96+52= 180

A=32 degrees -> 1st angle
B=96 degrees -> Second angle
C=52 degrees -> Third angle


It takes practice, but I use stuff like this as an engineer all the time. It gets easier.

Answer 3

angle one = x
angle two = 3x
angle three = 2x - 12

The sum of the angles of a triangle is 180 making the equation:
x + 3x + 2x - 12 = 180
solving: 6x - 12 = 180
6x = 192
x = 32

so the first angle is 32
the second angle is 3 x 32 which is 96
and the third angle is 2 x 32 - 12 which is 52

angle 1 = 32
angle 2 = 96
angle 3 = 52

Answer 4

How many degrees are in a triangle? 180
let us denote the first angle as x
let us denote the second angle as 3x
let us denote the third angle as 2x - 12
now:
x+3x+2x-12=180
6x-12=180
6x=192
x=32 degrees
angle 1= 32 degrees
angle 2= 96 degrees
angle 3= 52 degrees

Answer 5

let x = 1st angle
let 3x= 2nd angle
let 2x-12 = 3rd angle

x+3x+(2x-12) = 180
since there are 180 degrees in a triangle

add the common terms
6x-12=180

solve for x
6x -12=180
+12 +12
6x= 192
/6 /6
x=32

plug in x

1st angle= 32
2nd angle= 3(32)= 96
3rd angle 2(32)- 12= 52

Answer 6

f=first angle, s = second angle, t = third angle
f+s+t = 180 (degrees)
s=3*f
t=2*f-12
=>
(substitute second and third equations into first)
f+ 3*f + 2*f -12 = 180
6*f -12 =180
6*f = 192
f = 32
s= 3 * f= 3 * 32 = 96
t = 2 * f -12 = 2 * 32 - 12 = 52
Double-check angles, 32 + 96 + 52 = 180

Answer 7

First, write down what you think you see in the words. Then test to see if you got it right:

a + b + c = 180
3a = b
2a - 12 = c

Solve for any angle first. I'll take a:

a + 3a + 2a - 12 = 180
6a - 12 = 180
6a = 192
a = 32

Now solve for the other two angles:

3a = b
3 * 32 = b
b = 96

2a -12 = c
(2 * 32) - 12 = c
64 - 12 = c
c = 52

Check your answers:

32 + 96 + 52 = 180

Seems to work.

How do you always do this easily? Find out what you didn't know to be able to put that together yourself. Was it visualizing the problem? Mathematics starts with abstracts, but was created to think about concretes (I want to build a bridge, but I can't just grab tons of steel and experiment with it, so I'll take the idea of steel and experiment with that, and when I'm ready (the abstract is figured out), I'll start welding it together (I'll start working with the concrete).

Mathematics builds on itself. Your success with mathematics has more to do with how you study than how smart you are or anything else. It's just a preference of what you look at and work at. You can make exponential strides in your enjoyment of life and education with a commitment to the ideas in this article: http://www.ai.uga.edu/mc/WriteThinkLearn_files/frame.htm

Warm regards

Answer 8

Let's call the 3 angles a, b, & c....
And we'll assume each of our answers are in degrees.
We know that b=3a
And that c=(2a)-12 (or "c-12= 2a")(or "c-6=a")
We also know that (since it is a triangle) a + b + c =180
so [c-6] + 3[c-6] + c =180
or [c-6] + [c-6] + [c-6] + [c-6] + [c-6] + c=180

so 6c-36=180, or 6c =216, so c =216/6 = 36

Now we know that a + b + 36 =180, so a + b must = 144

Since b=3a, 144 must = 4a, so a= 36, and b= 108, and that leaves us with c=36

but I might be wrong since no-one else agrees...

Answer 9

angle 1 = 32
angle 2 = 96
angle 3 = 52

Answer 10

You have triangle angles a, b, c

b = 3a
c = 2a-12

But the most important part it's leaving out that it assumes you know is: a + b + c = 180.

All triangles must add up to having 180 degrees.

Therefore:
a + b (which is 3a) + c (which is 2a-12) = 180

Or

6a = 192

a = 32
b = 3a = 96
c = 2a-12 = 52

Sanity check:

a + b + c = 32+96+52 = 180 Still works!