1. Protractor Question

Hey Guys,

This question is confusing me a lot. It's telling me that those two angles are complementary so I have angle MNP + angle PNQ = 90

The answer in the back of the book is x = 143.

I can get 143 by adding 50 + 90 = 143 haha. But I've tried subtracting 92 - 53 and adding the answer to 92 and what not. It's just confusing me. Sounds simple but I don't know how to set this up.

2. Re: Protractor Question

Originally Posted by Cake
Hey Guys,

This question is confusing me a lot. It's telling me that those two angles are complementary so I have angle MNP + angle PNQ = 90

The answer in the back of the book is x = 143.

I can get 143 by adding 50 + 90 = 143 haha. But I've tried subtracting 92 - 53 and adding the answer to 92 and what not. It's just confusing me. Sounds simple but I don't know how to set this up.
you are told there are 90 deg between 53 deg and m. So add 90 deg to 53 deg to get 143 deg. That's all there is to it.

3. Re: Protractor Question

Oh, so do I ignore the 92? So there are numbers 92,53,and m. Why do I not touch the 92? Do I cover the 92 with a 90 instead?

4. Re: Protractor Question

Originally Posted by Cake
Oh, so do I ignore the 92? So there are numbers 92,53,and m. Why do I not touch the 92? Do I cover the 92 with a 90 instead?
the 92 is what's known in the vernacular as a "red herring". It's of no use solving this problem.

5. Re: Protractor Question

Originally Posted by romsek
the 92 is what's known in the vernacular as a "red herring". It's of no use solving this problem.
Sweet, I see now. Last question, what's the reason for adding 53 to 90? I understand the 90 part because of complementary angles. But, why add the 53? I just want to clearly understand it so I don't make these sort of questions again.

6. Re: Protractor Question

Originally Posted by Cake
Sweet, I see now. Last question, what's the reason for adding 53 to 90? I understand the 90 part because of complementary angles. But, why add the 53? I just want to clearly understand it so I don't make these sort of questions again.
you add the 53 because that's where you start from. The angle between 53 deg and m deg is 90 deg. Another way of looking at it is

m - 90 = 53, which immediately is solved as

m = 53 + 90 = 143

7. Re: Protractor Question

Ahhh, okay, okay. I get it. I see it now. I was getting so confused because of the image. You see, angle MNQ looks almost like a 90degree right angle judging from those black lines. I was so confused because of this.. I thought to myself, how can an almost 90 degree angle be a 143? I notice now that 143 IS m because the whole protractor is 180 degrees total. And m looks around the 143 mark.

8. Re: Protractor Question

Originally Posted by Cake
Ahhh, okay, okay. I get it. I see it now. I was getting so confused because of the image. You see, angle MNQ looks almost like a 90degree right angle judging from those black lines. I was so confused because of this.. I thought to myself, how can an almost 90 degree angle be a 143? I notice now that 143 IS m because the whole protractor is 180 degrees total. And m looks around the 143 mark.

MNQ is a 90 deg angle. That's what MNP and PNQ being complementary means. M=x is 143 because Q is at 53. If you start at Q and go counterclockwise 90 deg you arrive at M. So x is 53+90=143.