How to solve for the missing angle?

Solve for the missing angle between parallel lines. #math #maths #mathematics #shorts

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[AnonimityAssured]

This is what I would call a minimal-information problem. It's easy to solve in one's head by imagining either a symmetrical case or an extreme one.

[ignacioangelo]

I got to prove that blue and green amount to a total of 150° with a roundabout way of extending AB and BC. Got the same answer but your method is simpler. Thanks!

[apollosun]

The measure of Angle ADC = 60 degrees.
The sum of the internal angles of a quadrilateral is 360 degrees.
150 + 150 = 300
360 - 300 = 60

[lagazofamily]

Wait! Is there an indication that m<EAB = m<BAD and m<BCD = m<BCF? You should include these statements because it’s not clear in the drawing.

[jimparsons]

Liked the clip. Takes me back to when I took my High School Plane Geometry --- which still pops up every now and again --- those elegant solutions. Formalized logic. What an incredible tool! Perhaps the BCE Greeks' greatest gift to humanity? That's my take anyway. And obliviates any and all the Roman Empire did .

[tamaskovacs]

Interesting the fact, however the polygon is not defined exactly, but the angle at D always be 60, if the polygon satisfies the conditions for A and C angles.

[dragonsdream]

Dropping a perpendicular from B to F, then extending it to E gives you two right triangles, giving you (180-red-green+150 = 180) => -red-green = -150 => red + green = 150 so the ? angle is 360 -(150 + 150) [interior angles of a quadrilateral] which equals 60 degrees.

[TheEulerID]

Not the way I did it (I put a line normal to the parallel lines and through point D). I was able to produce two expressions for the value of the mystery angle that way and a+c=150 dropped out and then so did the value for the mystery angle of 0 degrees. Maybe not as neat, but it worked.

[derelbenkoenig]

Always feels nice to get the answer in a slightly different way. I drew the line perpendicular to the parallel lines and going through b, and then figured out the sum of the interior angles of the triangle made up by that. And that gave me the sum of green plus blue, which then applied inside the quadrilateral

[PrakharRSingh]

A lot of people would look at it and tell, it's 60°. 😂

[mathexin]

I drew a line from E to F. Now ABCFE is a pentagon, and the sum of the blue and green angles is 540-90-90-210 = 150 degrees. Then angle ADC is 360-150-150 = 60 degrees.

[bradey]

I did it a different way but yes this is a nice puzzle

[elliotingberg]

I made a shape with four corners in the bottom left where two angles were 90 degrees and 1 angle was 360 - 150, and 1 angle was half of C then i solved for C which was 75. And then by some luck (I didnt realise I didnt bisect) when i made a triangle BDC I just subtraccted 75 and 75 from 180 and got 30. Then I multiplied by two. I have no idea why this works since I didnt bisect. Can someone tell me if there is something mathematic behind this, if I'm lucky, or if I counted anything wrong.

[addct]

we can extendline AB to the CF parallel line to lets say point K... now in triangle BCF small angle A + small angle B + (180-150) = 180 degree as sum of all angles in a triangle is 180.... hence required angle = 360 - (150 + 150) = 60

[maxhagenauer]

I have a much more complicated way where you dont need to know any theorems or laws:

Call each green angle x and each blue angle y and call angle ADC z. So we have x + y + 150 + z = 360. Construct line EF, so in that inside shape, you have 90 + 90 + (180 - 150) + x + y = 360. Then because EA and FC are parallel, say 180 - 2x = 180 - 2y. So then you know that x and y are the same. So (x, y, z) = (75, 75, 60)

[geoninja]

I extended AD to the lower parallel line, formed a triangle with the supplementary angle of D. Ended up with simultaneous equations that showed the other angles added to 150 deg.... nice puzzle...

[sachiny]

That's the beauty of mathematics.. We can solve a problem in many ways...
I did it by extending AB or BC

[sqwt]

we had literally done a really similar problem yesterday in class and i know how to solve this 💀💀

[proximitymath]

I drew a vertical line through B and got 60

[topodemosaprender]

So basically the answer would be 360- 2(150)= 60