Triangles Make All Angles
Triangles Make All Angles
This lesson is premium only. Join us in the full course!
5:07

Triangles Make All Angles

536
Course In Progress

Triangles Make All Angles

536
Course In Progress
Marshall Vandruff
In this lesson, I'll break down how to use triangles to create accurate angles in 15-degree increments, covering angles from 0 to 180 degrees. I’ll demonstrate how flipping and combining simple 30/60 and 45/90 degree triangles can yield various angles, like 135, 120, 150, and even specific ones like 15 or 75 degrees. These techniques are practical for understanding angles in freehand perspective drawing without memorization, though familiarity with these increments can improve precision.
Newest
Sandra Salem
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.
Dermot
2d
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 :)
Christian Zinser
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!
Charlie Nicholson
Good catch! We'll swap it out soon!
Marshall Vandruff
It sure does! Thank you for noticing. We got ten degrees ahead and didn't notice... then skipped only 5° at finish line. This is why we need the likes of you in this group...
Brian Slavin
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
Charlie Nicholson
Good catch! We'll swap it out soon!
Marshall Vandruff
Indeed. Noted. We could claim it was deliberate to see if you were paying attention, but it would be a lie. It was a mistake. Thanks for pointing it out..
@jaejaelearning
how you stacked the two triangles in the isometric video explained! Woohoo! All becomes clear in time.
Amu Noor
6d
Question: Are these angles used in linear perspective as well as in isometric perspective?
Marshall Vandruff
We barely use this in Linear Perspective, but it makes sense to notice it early in training, as a foundation for how line angles can be quantified. And it's useful for sharpening your perception. It's a bit like ear training for a musician, or knowing the notes on the grand staff before improvising on an instrument.
Li Ming Lin
I had the same question as well. I was wondering if it is for Axonometric perspective or for Linear perspective? I feel it is the latter when experimenting with some cuboids. Because Axonometric perspective is perspective without vanishing points. Then as an example, if we make the center of the circle the vanishing point, then does it become one-point perspective? Sorry if it is an obvious question :D
Donna Milligan
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. 👍
Marshall Vandruff
Donna - the course isn't finished yet! We're producing part 2 now. If you feel like it's going too slowly, you may want to augment it by studying shading, which fits well with this one, or an unrelated subject to balance it. This is a long ride, usually with a week or two between assignments, as you apparently needed here. But it is by design that we are parsing these out...
Sarah NP
7d
Brilliant AND funny! Thanks Marshall.
@lucastoonz86
I like my compass but it does damage the paper. I used 22.5 degree increments on top and 15 degree increments on bottom.
Marshall Vandruff
You went all out. You also paid the price for the damage to the paper. Battle wounds to impress those who weren't there.
Katie
7d
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!
Marshall Vandruff
A rare gift. And you carried it through all the way. Thanks for posting.
Randy Pontillo
This 5 minute video taught me more about angles than the entirety of my school career
Marshall Vandruff
Thanks Randy and Lucie. I didn't know, when we recorded it, that it would be so "for you."
Lucie VERGNON
Same 🤣
Nassim A.
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 ^^')
Marshall Vandruff
Yay! Geometry Gamified.
John
7d
This was awesome, thank you Marshall. I tried using my triangles during the Isometic Optical Illusion homework assignment and was struggling in a dramatic fashion (many huffs and puffs). This was a very helpful illustration that I will practice a bunch!
Marshall Vandruff
Thank you John!
Martin Vrkljan
That joke... man, I did not expect that. I think I'm beginning to realize what a ride we're all in for with this course. Great stuff, Marshall!
Marshall Vandruff
Thanks Martin!
Johannes Schiehsl
Getting familiar with angles also comes in handy in navigation on land, sea and in the air.
Marshall Vandruff
Yaw. That's all about Yaw. In Lessons 7we'll get to Pitch, Yaw, and Roll...
Johannes Schiehsl
Concerning jokes: What do you call a triangle with no angle? - A nice try.
@dooby
8d
Anybody know were to buy that circular ruler thingy-mah-bob? It's looks really cool and now I want one
@ryanlloyddesign
It looks like a Helix Angle & Circle Maker. I got one from Hobby Lobby not too long ago.
Use Code BLACK20 to Save 20%
Course in Parts
View course details
Give a gift
Give a gift card for art students to use on anything in the Proko store.
Or gift this course:
About instructor
I Write, I Draw, I Teach
Help!
Browse the FAQs or our more detailed Documentation. If you still need help or to contact us for any reason, drop us a line and we’ll get back to you as soon as possible!