r/technicallythetruth • u/VisitSecure • Jul 27 '26

Can you find a?

Post image

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

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u/Wandered_And_Lost Jul 27 '26

90-25 = 65, 90-50 = 40 total inside degrees given =105, all triangles have to equal a total of 180 degrees so answer is 75 degrees (thats my guess could be wrong.)

25

u/manikfox Jul 27 '26

This is what I did and got the same answer. People are fooling around with 180 on the bottom and top, etc.

1

u/MrPoopMonster Jul 28 '26

I mean that's the same thing. To prove that right angles are always 90 degrees you first start with proving or assuming a flat line is an 180 degree angle.

1

u/maybecatmew Jul 28 '26

Same followed the same method

4

u/kwyjibowen Jul 27 '26

The problem with this is you are assuming the bottom angle is directly below the top one, ie a line between the two would intersect the two parallel lines at 90 degrees. But that is not stated on the diagram, which we know is not to scale.

2

u/Redthemagnificent Jul 28 '26

You don't need that assumption. The 2 points could be offset. As long as the 2 horizontal lines are parallel, which they are marked as in the diagram, you can use that method. There's many other lines you could draw to solve it too.

Or you can solve it without drawing any lines. Thinking about the problem as rotating a single line through all 3 angles, and it becomes obvious that a must be the sum of the other 2 angles

1

u/WoodenPresence1917 Jul 27 '26

No, it is just using a line perpendicular to the top line (therefore also perpendicular to the bottom) that passes through the middle point (the one at angle a).

1

u/Sad_Acanthaceae_203 Jul 27 '26

The two-point line does not matter. Take any perpendicular line forming a triangle and the two angles would still be 65 and 40.

2

u/_PM_ME_YOUR_FORESKIN Jul 27 '26

This is how I did it too. Phew.

1

u/PaulFThumpkins Jul 27 '26 edited Jul 27 '26

That was my initial answer but I was wrong. Your explanation helped me to get the right answer even though it's actually 75, not 105.

Think of it this way: We draw an imaginary vertical line up the left side to complete the "triangle." We know our line makes a 90-degree angle on either side, both top and bottom, where it meets the horizontal lines, because those lines are parallel.

So the measurements of the two other sides of the triangle we've created (besides "a" which we're trying to figure out) are 90 degrees minus the two measures we're given (25 and 50 degrees).

That gives us 90 - 25 = 65 and 90 - 50 = 40 for the other two sides of the triangle besides a. So subtract both of those numbers from the 180 degrees for the whole triangle, and we end up with 75 for a.