Discovering Acute Angle Between Two Planes in Basic Geometry | Learn with Gyazo

[phospho]

Hi,

Take a look at the image here: http://gyazo.com/ded6b502ad2e5766e485cf0fc8535d83

I want to find alpha (the acute angle between two planes), I have found theta, but how do I find alpha? My book states it's 180-theta but I don't get why.

 

[HallsofIvy]

It would help if you told us what the whole problem is! Given the information in your picture, you would certainly not be able to find theta! So there must be additional information you are not giving us.

Are n1 and n2 perpendicular to the two rays of the angle? The interior angles in any quadrilateral total 360 degrees. If n1 and n2 are perpendicular to the rays so they total 180 degrees, that leaves 180 degrees for theta and alpha: theta+ alpha= 180 so alpha= 180- theta.