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
J. Menriv
2d
Wondering if there are any major accuracy disadvantages to using the 'X trick' to find angles without a protractor or triangles.
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Sharon Cichelli
28d
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.
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Lynnette Jones
1mo
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?
Jay R
1mo
My drafting tools just arrived and I'm so frustrated because the bevels on the squares keep falling off the ruler when flipped upside down. Also the squares were cracked when Amazon delivered them.
Jay R
1mo
I feel like IF the ruler was not true parallel to the center line, then sliding the triangles along the ruler would cause the angles to be really off. I always have trouble finding dead center of a circle.
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@elzepeda
1mo
Happy I took trig
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Jacob Granillo
3mo
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
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Jacob Granillo
3mo
Did it!
@zeeillustrates
3mo
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!!
Ethyn
3mo
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.
Ramzi Chamcham
3mo
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.
Sandra Salem
3mo
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.
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Dermot
3mo
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
:)
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Christian Zinser
3mo
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!
•
3mo
Good catch! We'll swap it out soon!
•
3mo
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
3mo
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
•
3mo
Good catch! We'll swap it out soon!
•
3mo
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
3mo
how you stacked the two triangles in the isometric video explained! Woohoo! All becomes clear in time.
Amani Noor (Amu)
3mo
Question: Are these angles used in linear perspective as well as in isometric perspective?
•
3mo
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
3mo
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
3mo
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. 👍
•
3mo
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...
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Sarah NP
3mo
Brilliant AND funny! Thanks Marshall.
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@lucastoonz86
3mo
I like my compass but it does damage the paper. I used 22.5 degree increments on top and 15 degree increments on bottom.
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3mo
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
3mo
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!
•
3mo
A rare gift.
And you carried it through all the way. Thanks for posting.
Randy Pontillo
3mo
This 5 minute video taught me more about angles than the entirety of my school career
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3mo
Thanks Randy and Lucie. I didn't know, when we recorded it, that it would be so "for you."
Lucie VERGNON
3mo
Same 🤣
Nassim A.
3mo
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 ^^')
•
3mo
Yay! Geometry Gamified.
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I Write, I Draw, I Teach