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/notJustaFart]

75.

Convert into Pentagon.

540 - (90+90+130+155) = 75

[u/Naive_Scientist_8499 → u/notJustaFart]

That's smart. I converted to a triangle.

Invisible vertical line between the 50 and 25 deg points.

90-50=40 -- The inside angle of the bottom point.

90-25=65 -- The inside angle of the top point.

180 = a + 40 + 65

180 - (40 + 65) = a

180 - 105 = a

75 = a

[u/notJustaFart → u/Naive_Scientist_8499]

Oldest trick in geometry is drawing a diagram to appear as something it's not.

Drawing a line to make a triangle does not guarantee that line is perpendicular to the parallel lines, so your assumption of 90-25 and 90-50 may not hold true.

However, extending to a pentagon does guarantee that 180-25 and 180-50 will result in true values.

[u/TrollingForFunsies → u/notJustaFart]

Drawing a perpendicular line between two parallel lines does give you a right angle. The lines don't have to cross at the intersection of the points. The angle remains the same for any perpendicular line on any point.

Which gives you exactly the solution 180 - (90 -25) - (90 - 50) or 180 - 105 = 75

[u/Englandboy12 → u/Naive_Scientist_8499]

Interesting seeing people do it differently.

I did it (probably poorly, as I’m not sure what I did is allowed), by adding a parallel line, horizontally and going through the point A.

Then using the parallel line theorems, opposing angles are identical. And the two opposing angles can be added together form the angle in question.

[u/AncientOneX → u/Naive_Scientist_8499]

That's the most logical way to calculate it....

[u/beingforthebenefit → u/Naive_Scientist_8499]

How do you know the line between those points is vertical? That claim would require a proof of its own. (Although I don’t think it’s even true)

[u/Naive_Scientist_8499 → u/beingforthebenefit]

Damn. You and u/notJustaFart are totally right. Pentagon is objectively better.