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
1d
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
3d
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!
Brian Slavin
6d
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
@jaejaelearning
6d
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?
Donna Milligan
6d
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. 👍
Sarah NP
7d
Brilliant AND funny! Thanks Marshall.
@lucastoonz86
7d
I like my compass but it does damage the paper. I used 22.5 degree increments on top and 15 degree increments on bottom.
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!
Randy Pontillo
7d
This 5 minute video taught me more about angles than the entirety of my school career
Nassim A.
7d
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 ^^')
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!
Martin Vrkljan
7d
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!
Johannes Schiehsl
8d
Getting familiar with angles also comes in handy in navigation on land, sea and in the air.
@dooby
8d
Anybody know were to buy that circular ruler thingy-mah-bob? It's looks really cool and now I want one
Use Code BLACK20 to Save 20%
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