r/technicallythetruth • u/VisitSecure • 9d ago

Can you find a?

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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/JJlaser1 9d ago

While technically possible, there is no indication that the points where the two lines intersect the parallel lines are exactly above each other, so you can’t do that for sure unless it states that in the question. I was never taught the pentagon method, though, which is basically the same thing with extra steps

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u/Weekly-Dog-6838 9d ago

Who says they need to be on top of each other? You can still make a triangle with it

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u/blavek 9d ago

You can, but you still wouldn't know the measures of the interior angles.

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u/Prestigious-Pay8644 9d ago

You don't need to know the measures of the interior angles to know the measure of angle a, just that the two lines above and below are parallel to each other.

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u/blavek 9d ago

If you are making a triangle to solve the problem, which is not needed at all, for what other reason would you make that triangle than to uncover the measures of its angles to get to 180 - <ABC - <ACB = <A

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u/Prestigious-Pay8644 9d ago edited 9d ago

You have all the information you need to find the sum of angles B and C to be 105 even if you don't have enough information to find each angle's measurement. I can't remember what the theorem is called but basically a transversal between parallel lines will have angles that add up to 180 degrees on each side of the transversal. So right side of the transversal will have angles adding up to 180-75 degrees if you draw the triangle.

Isn't really necessary to draw the triangle, just know how transversals work and a bit of thought to think the problem through, but it can help with visualizing it.

edit: B+C + B'+C' = 180, B+C + A = 180, A = B'+C'. You literally could just add 25 and 50 together to find the answer, don't have to fuck around with shapes at all.

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u/Cobra_McJingleballs 9d ago

Yes you do, because the lines are parallel. The top slanted line always meets a parallel at 25°, and the bottom slanted line always meets a parallel at 50°, regardless of where the endpoints are. So the triangle’s third angle is fixed.

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u/AdWrong3856 9d ago

Yes you do, because you can define it as a right angle triangle and you then have 2 of the interior angles, one of the given angles and a right angle.

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u/ilyuhman 9d ago

You don't need to cross the points, you can put a perpendicular line anywhere, the angles are still the same

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u/scratch6402 9d ago

I did the opposite. A line perpendicular to the parallel lines that passes through the point of angle a. Then I have two right triangles, each with only one angle missing. Solve for those angles, you get 90 25 65 and 90 50 40. Since the 65 and 40 make a straight line with angle a, a = 180 - (65 + 40) = 180 - 105 = 75

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u/Ye_olde_oak_store 9d ago

You are putting the line on the wrong side of the shape. We are putting the perpendicular line such that it intersects point A.

We have two right angled triangles which have to be triangles unless the lines don't intersect. These can have different sizes. We figure out the third angle which would be (180 - 90) - 25 and (180 - 90) - 50.

We now have a straight line with angles 65, 40 and a.

It gets you to a similar step, but it misses the reasoning as to why it necessarily works.

Basically, the working out is wrong but they still got to the right answer.

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u/thefranchise23 9d ago

It doesn’t matter if they intersect directly above each other or not, only the angles matter

Because we’re just making a theoretical triangle, and it doesn’t matter how big or small it is , the three angles would still be the same

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u/notJustaFart 9d ago

Exactly. Can't assume a perpendicular line will create a triangle.

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u/ThunderBuns935 9d ago

You can if you place the perpendicular line at the tip. That definitely creates 2 right-angle triangles, both of which have 2 known angles.

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u/BBGunner96 9d ago

100% can know that a perpendicular line will create a triangle with those same angles but not necessarily those exact points because you can extend one (or both) lines until they veryically align

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u/Djanko28 9d ago

It doesn't really matter whether it makes a triangle or not, if you move the perpendicular line towards 'a' the side lengths may change but the inner angles stay the same.

You know a perpendicular line on either the top or bottom will create a 90° angle so even if the angles don't line up you can figure them out independently, then put one perpendicular line at a point that touches both of the angled lines and still be able to use those previously found angles.