Question

Fine the measure of angle ABC?

Please see image below.. Any help would be amazing

http://i58.tinypic.com/9aqnnc.jpg

a. 124
b. 97
c. 56
d. 51

Answer 1

What do you know about the measures of the three angles of a triangle?

Answer 2

angle a is 32 degrees? I'm sorry if that is a dumb reply..

Answer 3

angle b is 2x - 15 degrees... angle c (x - 5) degrees

Answer 4

Yes. The measure of angle A is 32 degrees.

This is the information you get form the figure:
m<A = 32 deg
m<B = x - 5
m<C = 2x - 5

Answer 5

The question I asked above is a general question about any triangle.
For any triangle, what do you know about the measures of the three angles?
Specifically, do you know what is the sum of the measures of the angles of a triangle?

Answer 6

oh.. yes sum is 180 degrees. so I know that i subtract 180 - 32 = 148

Answer 7

Good.
You know the sum is 180 degrees.
Now write the sum of all three angles and set the sum equal to 180 degrees.

Answer 8

sorry i meant to say i would ADD.... not subtract. ADD 15+ 5= 20

Answer 9

\(\color{red}{m\angle A} + \color{green}{m\angle B} + \color{blue}{ m\angle C} = 180\)

\(~~~ \color{red}{32} ~~+ \color{green}{x - 5} + \color{blue}{2x - 15} = 180\)

Answer 10

There is nothing here given as 5 or 15
We have an angle measure that is 32.
Another angle measure is x - 5.
The third angle measure is 2x - 15.

Answer 11

You can't separate the x or 2x part of the angles from the -5 and -15 parts.

Answer 12

ok

Answer 13

yes I see that part: 32 + x - 5 + 2x - 15 = 180

Answer 14

Since the angles are 32, x - 5, and 2x - 15, now we add those amounts together.

The sum of the measures is:
32 + x - 5 + 2x - 15

We know the sum of the measures of the angles of a triangle is 180, so we set the expression above equal to 180.

32 + x - 5 + 2x - 15 = 180

Answer 15

Ok, I see you understand it now.

Answer 16

The last line is an equation with only one variable, x.
We can solve for x.

Answer 17

but.. i'm confused about what to do with the 5 and 15 part of the equation. I know that helps me solve for x

Answer 18

We'll go over solving the equation together.

This is the equation:
32 + x - 5 + 2x - 15 = 180

Answer 19

The first step is to combine like terms on the left side.
Like terms are terms that have the same variable part.
The variables are the letters.
In our case, there is only one variable, x.

Answer 20

yes i now..understand that part

Answer 21

In our equation, on the left side, the like terms are:
1) x and 2x are like terms bec they both have x.
2) 32, -5, -15 are like terms bec they are only numbers.

Answer 22

Ok.. NOW that makes sense

Answer 23

so.. 32 - 20

Answer 24

Now we combine the terms with x:

\(32 + \color{red}{x} - 5 + \color{red}{2x} - 15 = 180\)

\(\color{red}{3x} + 32 - 5 - 15 = 180\)

Answer 25

You are correct. I did the x's first. Now I'm doing the numbers.

Answer 26

\(3x + \color{blue}{32 - 5 - 15} = 180\)

\(3x + \color{blue}{12} = 180\)

Answer 27

can i ask a stupid question? how does 2x + x = 3x ? is it because x is 1?

Answer 28

First, your question is not stupid.
By asking questions you learn.

Answer 29

so... 3x + 12 = 180, then... 3x = 168

Answer 30

how i got to that.. was subtracting 12 from 180. so that would be 168.

Answer 31

Mathematicians are lazy.
They like to write as little as possible.
x means the same as 1x
That is why 2x + x = 3x, it's because
2x + x = 2x + 1x = 3x.

Answer 32

Correct.
3x = 168
Now divide both sides by 3 to get
x = 56

Answer 33

Got it! so in any case.. where you have just 'X'... such as x + 5... then the value is always going to be 1x

Answer 34

ok.. wow.. your awesome.. I get it now. thank you thank you

Answer 35

Now we know what x is.
Angle ABC is the same as angle B.
We are told m<B = x - 5
We know x = 56, so
m<B = x - 5 = 56 - 5 = 51

Answer 36

Yes, you are correct.
An expression such as x + 5 means 1x + 5

Answer 37

that is what was throwing me off so much

Answer 38

Now you know it.
Keep studying and asking questions.
That's how you learn.