Geometry help

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rachelmaddie

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In this figure, KJ and KL are opposite rays. <1 is equal to <2 and KM bisects NKL.
If m<LKN = 7q + 2 and m<4 = 4q - 5, what is m<3?

So far I have 7q + 2 = 2(4q - 5)
 

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7q + 2 = 8q - 10

I don’t understand the next step how to get the variables on the one side.
 
Try adding [MATH]10-7q[/MATH] to both sides...what do you get?
 
Okay, the first add 10 to both sides, and then subtract 7q from both sides...
 
rachelmaddie said:
7q + 2 = 8q - 10

I don’t understand the next step how to get the variables on the one side.
Click to expand...
Please do not forget your algebra. Did someone tell you that it would be unnecessary in Geometry? That would be wrong.

Algebra 1 - Solve for q
7q + 2 = 8q - 10

Go!
 
rachelmaddie said:
No, now that I know the value of q, I’m suppose to find the measure of m<3.
Click to expand...
That's very good.

With the value of q, you can calculate the measures of the two angles that got us here. From there, you can find the measure of the desired angle. Let's see your calculations.

Let's also note:

7q+2 = 7(12)+2 = 84 + 2 = 86
4q-5 = 4(12)-5 = 48 - 5 = 43

Do those look reasonable? Could they be the measures of the given angles?
Reality Check: Not all drawings are perfect or even helpful.
 
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tkhunny said:
That's very good.

With the value of q, you can calculate the measures of the two angles that got us here. From there, you can find the measure of the desired angle. Let's see your calculations.
Click to expand...
I’m stuck on this.
 
This is where we need to start putting things together. It is this moment that will define your mathematics career, no matter how long or short it is or may be. You have to start seeing the pathway between where you are and where you need to be - what you have or know and what you need to know (or don't have). The teaching of mathematics is not just to force you to memorize things. It is also not to have someone else tell you exactly what steps to take to accomplish solutions to problems. Part of the teaching of mathematics is to help you learn some abstraction and some linear thinking and some logically ordered processing. All these things will save you later in life. You don't have to be the best linear thinking on the planet, but you do need some skill in this area to survive in today's society. This is one reason why we study mathematics.

Now, let's think.

1) We have m<LKN
2) We have m<4
3) We do not have m<3. How can we get it?
 
rachelmaddie said:
86 - 43 = 43?
Click to expand...
Here's the problem with that response: "?".

Are you sure? If not, why not? What does "bisect" mean? Even without "bisect", what is the relationship between <LKN, <4, and <3?

You tell me if that is correct. No "?"!

This is another one of the useful things in the teaching of mathematics. Words mean things. The word "bisect" has a definition. It's not squishy. It's not morally flexible. It's definition is reliable. We don't have to ask, every time we see it, if it means the same thing it meant the last time we encountered it. Try doing that with a novel by Franz Kafka!
 
rachelmaddie said:
In this figure, KJ and KL are opposite rays. <1 is equal to <2 and KM bisects NKL.
If m<LKN = 7q + 2 and m<4 = 4q - 5, what is m<3?

So far I have 7q + 2 = 2(4q - 5)
Click to expand...
1568048314621.pngWe see <LKN = <3 + <4

m<3 = (7q + 2) - (4q + 5) = 3q + 7 = 3*12 + 7 = ??
 
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