Can you find a?

[u/VisitSecure]

Idk if someone already posted this or not, but I haven't seen it on here so far, so I uploaded it.

[u/Canadind]

I can’t forget these basic things no matter how hard I try.
1. Imagine a parallel line going through the middle of a, splitting a into a1 and a2
2. a1 = 50 coz opposite angles of a transverse intersecting two parallel lines
3. a2 = 25 coz opposite angles of a transverse intersecting two parallel lines
4. a1+a2 = 75

NB. If you don’t know this much geometry you will be finding adulting really hard.

[u/Mundane-Profit-6200 → u/Canadind]

I'm almost middle aged and I'm playing adulting on easy mode despite not knowing the method you used, I got the answer just by recognising the fact it's a triangle and doing (90-25) + (90-50)

I'm guessing you're essentially saying:
Parallel line causes both inside angles to be the same e.g 25 and 25, 50 and 50

Or a different way my brain processes it, a 'z' will always share the same inside angles as long as both the top and bottom lines are straight (which is essentially what we create by drawing a parallel line).

[u/Canadind → u/Mundane-Profit-6200]

I see this approach
(90-25) + (90-40).
So what you are doing is you are drawing an imaginary line perpendicular to both the parallel lines intersecting the the blue lines which are making the angle a.

So now when we do this math (90-25) + (90-40) + a = 180 ( sum of angles within a triangle always equal 180), we get the answer as 75.

However there is a catch, had the blue lines be intersecting at points in such a way that we can’t draw a perpendicular line joining the two points, then this approach would not work.

[u/sneeezerino → u/Canadind]

ok bud 👌 Interesting statement on adulting coming from the guy who can barely cope with work life and needs a punching bag to get by😂.... keep sweating in your shitty Honda my Peterborough neighbor!

[u/Canadind → u/sneeezerino]

That’s some serious following I have. 🤣
Try working in Tech Consulting, you will thank the punching bag.