# Project: Second Chapter of Geometry Book

**URL:** <https://discuss.criticalfallibilism.com/t/project-second-chapter-of-geometry-book/385>\
**Category:** Projects\
**Tags:** math\
**Created:** [November 2, 2021, 2:17am UTC](https://discuss.criticalfallibilism.com/t/project-second-chapter-of-geometry-book/385 "2021-11-02T02:17:49Z")\
**Posts on this page:** 4\
**Page:** 3

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**Author:** ![JustinCEO](https://discuss.criticalfallibilism.com/user_avatar/discuss.criticalfallibilism.com/justinceo/32/9_2.png) [@JustinCEO](https://discuss.criticalfallibilism.com/u/JustinCEO)\
**Post date:** [December 10, 2021, 3:07am UTC](https://discuss.criticalfallibilism.com/t/project-second-chapter-of-geometry-book/385/41 "2021-12-10T03:07:28Z")

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I looked at a workbook of simple systems of equations exercises. The workbook quality was iffy but I practiced some anyways. I am definitely rusty. I tried tackling 2.57 again but it’s trickier than the workbook stuff (which had e.g. 3 equations of 3 variables all nicely laid out for you).

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**Author:** ![JustinCEO](https://discuss.criticalfallibilism.com/user_avatar/discuss.criticalfallibilism.com/justinceo/32/9_2.png) [@JustinCEO](https://discuss.criticalfallibilism.com/u/JustinCEO)\
**Post date:** [December 10, 2021, 3:08am UTC](https://discuss.criticalfallibilism.com/t/project-second-chapter-of-geometry-book/385/42 "2021-12-10T03:08:13Z")

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One issue that I find I have is going in circles proving stuff I already know instead of making progress on the problem.

EDIT: I meant that I had that issue specifically for Exercise 2.57 above.

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<div class="post-metadata">

**Author:** ![JustinCEO](https://discuss.criticalfallibilism.com/user_avatar/discuss.criticalfallibilism.com/justinceo/32/9_2.png) [@JustinCEO](https://discuss.criticalfallibilism.com/u/JustinCEO)\
**Post date:** [December 10, 2021, 3:34am UTC](https://discuss.criticalfallibilism.com/t/project-second-chapter-of-geometry-book/385/43 "2021-12-10T03:34:00Z")

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Finally solved it.

We said x + y = b  
We are given b - c = 42°  
Because of how exterior angles work, x = y + c, which we can also represent as x - c = y

substitute x + y for b in b - c = 42°  
(x + y) - c = 42°  
Rearrange the above:  
(x - c) + y = 42°  
Substitute y for (x - c)  
y + y = 42°  
simplify  
2y = 42°  
divide by 2  
y = 21°

y is the ∠RQZ they were asking for. 🎉

The part that I was having trouble understanding in their answer basically just says x = y + c, but it’s harder to read so I wasn’t following.

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<div class="post-metadata">

**Author:** ![JustinCEO](https://discuss.criticalfallibilism.com/user_avatar/discuss.criticalfallibilism.com/justinceo/32/9_2.png) [@JustinCEO](https://discuss.criticalfallibilism.com/u/JustinCEO)\
**Post date:** [December 10, 2021, 2:40pm UTC](https://discuss.criticalfallibilism.com/t/project-second-chapter-of-geometry-book/385/44 "2021-12-10T14:40:54Z")

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Thanks to @ingracke and @Elliot for their help in solving Exercise 2.57. 🙏

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