Wondering if there are any major accuracy disadvantages to using the 'X trick' to find angles without a protractor or triangles.

To make your own triangles: For the 30-60-90 triangle, the hypotenuse is twice the length of the short side. For example, I drew an L with a known good 90-degree angle; measured 10 cm for the short side; and then used my ruler to find where a 20-cm diagonal line would complete the triangle. (The other leg is 10 cm times the square root of 3, but you don’t have to measure or compute that. Just connect the dots.) For the 45-degree triangle, both legs are the same length. (I used 15 cm for mine.) I made a cardboard straightedge to complete the set but didn’t even bother being fussy about whether its edges are parallel to each other; I just needed a straight line to rest the triangles on.

Is anyone else having trouble figuring out how to use the two triangles and ruler to get all the angles drawn? I'm having a bit of trouble following the video. Specifically where do I place the ruler and the two triangles?

Happy I took trig

This really helped me to get the angles correct. I struggled to use my materials when we did the optical illusions assignment, because I never used them before! I felt like I did enough circles for today, the fourth will I will do tomorrow

I haven't had this much fun in a while, Im going to try and do this every day or every once in a while until I have at least internalized most of angles. Just from this, I know that 120 corresponds to 300 so there's a start!!

Putting in some practice, getting used to using the triangles! I noticed I need to be more careful with where the lines start and end when being this precise.

I only did this due to the fear caused by the state of existential uncertainty that the joke put me in. Also, why does my T square kinda suck? It has no measurements, and slightly lifted off the table.

It was interesting. Nice exercise to undust all that geometry from Elementary. I did all the angles with the triangles, adding and subtracting. To be honest I rely on this little friend at the end to make life easier. Nonetheless I am pretty confident now, that if I find myself stranded on an island I won't die for a lack of shelter. This was worth my Google search: Ecclesiastes 4:9-12. Two are better than one, because they have a good reward for their toil. For if they fall, one will lift up the other; but woe to one who is alone and falls and does not have another to help. Again, if two lie together, they keep warm; but how can one keep warm alone... 😂 By the way, your jokes are awesome! Keep working on that comedic material.

Marshall, that's brilliant video lesson loved it! Who would have guessed that you invented the antique monochrome test card ! The 15 degree pizza, that's my wife's portion ! Thanks :)

Hi Marshall, great lessons so far, I'm really excited about studying perspective!! Who new that was possible... I guess I just needed to find a great teacher! I might be getting something wrong but I believe there is a mistake in the angles in the video, it skips from 105 to 130 and goes on from then. Here is a screenshot and I also attached my attempt at the angle wheel. Thanks for sharing!

Hi Marshall, I have watched this one a few times. I’m not good at math so I need to get it through my thick skull. FYI, when you are doing the pizza analogy the 15 degree angles are off beyond the 105 degree. cheers, brian

how you stacked the two triangles in the isometric video explained! Woohoo! All becomes clear in time.

Question: Are these angles used in linear perspective as well as in isometric perspective?

Thank you! I’ve been floundering with these triangles trying to figure out what you were doing for 2 weeks. I’m also the slightest bit concerned that the course isn’t finished yet and you’re stalling for time. Hopefully not, I’m in for the whole ride no matter what. 👍

Brilliant AND funny! Thanks Marshall.

I like my compass but it does damage the paper. I used 22.5 degree increments on top and 15 degree increments on bottom.

My supernatural ability to do math only as it pertains to art is constant. I found myself having so much fun puzzling triangles together that I kept going, haha!

This 5 minute video taught me more about angles than the entirety of my school career

To better understand this lesson, I tried to find on my own ways to add the 15° increments using only 45° and 60° squares. My brain melted.. But it was interesting to find out that there are several ways to get the same angles! (at least if I did it right ^^')