# High School Geomtry Problems

• Sep 21st 2013, 10:12 AM
Iceycold
High School Geomtry Problems
Hey, I have these 3 problems that I need to make sure I can do right for an exam Monday.

Here's are the three: (screenshots)

Screenshot by Lightshot

Screenshot by Lightshot

Screenshot by Lightshot

I've tried to do them but had no success. Here's what I did for each problem:

Problem 1: I didn't try for x, but I tried y. So we know all the interior angles add up to 180. So, (y+8) + 74 + x (where x is the top angle) = 180. Solve for y: y + 84 + x = 180. y+84=180 - x. y=96-x. And there I'm not sure where to go since it's not one of the answers. If I solve for y without the x, I just get 96 and that isn't an answer either.

Problem 2: Ok so I know if the two lines are parallel, the same side interior and exterior angles are supplementary to each other. So can't I just take one of the expressions, say angle 3, 8x + x (where the other x is the supplementary angle, angle 4) and solve for x? I tried that: 8x+x=180 9x=180 x=20, but 20 isn't in the answers.

Problem 3: For this problem, my teacher explained it the last 5 minutes of class so I didn't really get to take notes on it. I know that within the 2 parallel lines 2 triangles form and the 56 degree angle is part of a 360 circle. I just need to know how to work it out.

Thanks.
• Sep 21st 2013, 11:15 AM
emakarov
Re: High School Geomtry Problems
Quote:

Originally Posted by Iceycold
Problem 1: I didn't try for x, but I tried y. So we know all the interior angles add up to 180. So, (y+8) + 74 + x (where x is the top angle) = 180.

Do not redefine x. The value of x is defined by the picture: x - 3 is the leftmost angle. There is no reason to believe that x is also the top angle.

I am afraid, this is an ill-posed problem because the only restriction is (x - 3) + 41 + (y + 8) = 180 (one equation with two unknowns). Here y + 8 can vary between 0 and 180 - 74 = 106 degrees (exclusive). Each value of y defines x uniquely, but without additional information, such as that the triangle is isosceles, I don't see why y has to be unique. In other words, the vertex of the 41 degrees' angle can slide left or right.

What do the arrows represent? Is this the path of light reflecting from the horizontal line by chance? Then x - 3 = y + 8, but this does not fit any answer either...

Quote:

Originally Posted by Iceycold
Problem 2: Ok so I know if the two lines are parallel, the same side interior and exterior angles are supplementary to each other. So can't I just take one of the expressions, say angle 3, 8x + x (where the other x is the supplementary angle, angle 4) and solve for x?

Here you are redefining x again. The picture defines x as 1/22th of angle 8 (which, by assumption, is the same as 1/8th of angle 3). It is incorrect to say that x equals angle 8. Instead, angle 3 + angle 8 = 8x + 22x = 30x = 180 degrees.

Quote:

Originally Posted by Iceycold
Problem 3: For this problem, my teacher explained it the last 5 minutes of class so I didn't really get to take notes on it.

Continue the bottom inclined line to the intersection with line l. Then 56 is an exterior angle to the resulting triangle and, as such, equals the sum of the two interior angles adjacent to l.
• Sep 21st 2013, 02:03 PM
Iceycold
Re: High School Geomtry Problems
For problem 1 I beleive the the arrows represent congruency?

I sort of understand what you did for problem 2, buy why add the two expressions? Aren't the 2 supplementary angles the ones I highlighted below?

Screenshot by Lightshot

For problem 3 I have worked this thus far:

Screenshot by Lightshot

It's funny, I've done all these things in class but I just get confused here cause I have to look carefully for all the angles and extending lines etc..
• Sep 21st 2013, 02:28 PM
emakarov
Re: High School Geomtry Problems
Quote:

Originally Posted by Iceycold
For problem 1 I beleive the the arrows represent congruency?

Congruency of what?

Quote:

Originally Posted by Iceycold
I sort of understand what you did for problem 2, buy why add the two expressions? Aren't the 2 supplementary angles the ones I highlighted below?

Yes, 3 and 4 are supplementary, but so are 3 and 8 as interior angles of a transversal.

For problem 3, x and one of the 28's are alternate interior angles, so they are equal.
• Sep 21st 2013, 02:57 PM
Iceycold
Re: High School Geomtry Problems
For problem 1 I went over my notes and those little signs mean parallel and they keep going according to my teacher. Here, I've drawn it out on paper what it's supposed to look like to solve: Screenshot by Lightshot

I see what you mean about problem 2, I had that written down in my notebook. It just didn't seem right because it doesn't look like a traditional pair of angles like so: http://www.mathsisfun.com/geometry/i...ary-angles.gif

Okay, think I have problem 3 solved, this look right? Screenshot by Lightshot

Thanks for the help so far.
• Sep 21st 2013, 03:14 PM
emakarov
Re: High School Geomtry Problems
Quote:

Originally Posted by Iceycold
For problem 1 I went over my notes and those little signs mean parallel and they keep going according to my teacher.

This changes things. Then x - 3 = 74 as corresponding angles, and from (x - 3) + 41 + (y + 8) = 180 you can find y.

Quote:

Originally Posted by Iceycold
I see what you mean about problem 2, I had that written down in my notebook. It just didn't seem right because it doesn't look like a traditional pair of angles like so: http://www.mathsisfun.com/geometry/i...ary-angles.gif

There are many equalities related to parallel lines. You can explore them on the site I linked to.

Quote:

Originally Posted by Iceycold
Okay, think I have problem 3 solved, this look right?

If you used equality of alternate interior angles to conclude that the lower left angle is 28 degrees, then you can use the same principle to immediately conclude that upper left 28 equals x. Then you won't need to subtract stuff from 180.
• Sep 21st 2013, 05:32 PM
Iceycold
Re: High School Geomtry Problems
Okay, so for problem 1: Where did you get that 41 from?

And problem 2: I see, they are indeed supplementary but they don't share a vertex therefore they aren't a linear pair. That's why they don't look like that picture I linked. Got it.
• Sep 22nd 2013, 12:02 AM
emakarov
Re: High School Geomtry Problems
Quote:

Originally Posted by Iceycold
Okay, so for problem 1: Where did you get that 41 from?

From your original picture in post #1.
• Sep 22nd 2013, 07:52 AM
Iceycold
Re: High School Geomtry Problems
Excellent, I found x and y. For y, I solved the equation you gave and for x, since I knew x-3=74 due to corresponding angles, I just solved that equation for x.

Thanks for the help.