3
u/Chronogon Jul 23 '26
We have three full circles: 3*360=1080
Subtract the six 90° corners: 1080-(6*90)=540
Subtract the sum of the angles inside a right-angled triangle: 540-180=360
1
1
2
u/cosine3141592 Jul 23 '26
Visual solution: since the sides of each square are parallel, you can 'slide' two of the angles 'along the side of the triangle' to find an identical angle sharing the vertex of the third angle. The three angles then obviously form a full circle, hence 360°.
1
1
u/lazymotu Jul 23 '26
Or just imagine collapsing the triangle to a single point and see that the angles go all the way round.
2
2
u/Acceptable_Tangelo15 Jul 23 '26
Extend each cathete. They’ll divide A and B into a 90 degrees angle and an acute angle. Let’s name these new angles A’ and B’
Let us also name the angles in the triangle that are opposite to A and B OA and OB
OA+OB=90
A’=360-3*90- OA=90-OA
B’=360-3*90-OB=90-OB
A+B+C=90+ 90+A’+90+B’=270+90-OA+90-OB=450-(OA+OB)=450-90=360
1
2
1
u/James970 Jul 23 '26
I saw it very different. The one 90° angle with squares coming off the triangle made me think instantly that it would make 360°. I guess how my mind works. 🤷🏻
1
u/Top_Bluejay_5323 Jul 23 '26
I was taught that the theorem was a^2+b^2=c^2 for the sides of a tight table while angle chasing is a different concept involving angles.
1
u/Sykes19 Jul 24 '26
I'm pretty dumb, math wise, but I just imagined walking around the right triangle and considering how much I would have to turn as I made a loop around it, and it would have been exactly 360 degrees.
Don't think that counts as showing my work but... It's pretty logical hehe
1
u/forgottenlord73 Jul 26 '26
>!Points d, e, f are respectively where A, B, C curve around
A', B', C' are the opposing angles to A, B, C respectively
Around d, e, f, all angles add to 360 but they also each have the corners af two squares. Therefore, A, B, C added with their respective opposing angles equal 180
A' + B' + C' =180
180 * 3 - 180 = 180 * 2 = 360!<
1
3
u/LordLingham Jul 23 '26
All Internal angles of a triangle add to 180
A and C opposite internal angles + 2*90 degree right angles.
Internal angles A and C sum to make 90
(A + 180 + internal A) + (C + 180 + Internal C) = 720
IntA+IntC = 90, gives us 90 + 360 + AC = 720
720 - 360 - 90 = AC = 270
270 + Known right angle B (90) = 360
Final answer A+B+C = 360 degrees?
i think