If

Question

If <MLN = 41 degrees, what is the measure of <NLK? http://i.imgur.com/U8RbQYI.png?1 I need to know how to do these problems if you dont want to you dont have to use this problem.

mstoldegon · Answer

If you didn't know already, angle MLK is 90 degrees. Although it doesn't look like it (at least the way it is drawn), the little square in the corner next to L indicates it is a Right Angle - meaning it is 90 degrees. Since angle MLN is 41 degrees, angle NLK is 90-41.
   Did that answer your question?

anonymous · Answer

that did thank you! im still a little confused on how to do the ones without the little square though

mstoldegon · Answer

All of the inside angles of the four corners of polygon KLMN add up to 360 deg. This is a rule.
   We do know that KLM is 90 BUT to determine any other angles, other than the three we already know (KLM, MLN and NLK), we would have to know more.
   Either we need one of the other angles within triangles KLN and NLM to solve this geometrically, or we need the lengths of some of the sides and the diagonal to solve this Trigonometrically. Or a combination of both angles and lengths.
   Do you have any more data?

anonymous · Answer

If http://i.imgur.com/85R845J.png... that is all they give me, but ones like this im confused, every angle is different, i am just curious on the formula to do these types of problems

mstoldegon · Answer

To clarify, polygon LKMN has four sides. The inside angles of any four-sided polygon (square, parallelogram, trapezoid, etc.) always add up to 360 degrees.
   Polygons of four or more sides are often divided up into triangles because the three corners (or coordinates if used) and the three sides of a triangle are always in one single plane (or co-planar). The four (or more) points (or coordinates) of a polygon may not necessarily be co-planar.

mstoldegon · Answer

Didn't see you next question. Having problems losing connection with OpenStudy today.

mstoldegon · Answer

XYZ is a straight line but if you think of it as an angle, it is a 180 deg angle.
TYV will be equal to XYZ (180) minus TYX (116).

mstoldegon · Answer

Be back shortly.

anonymous · Answer

is there a universal way to do all of these types of problems or it just depends?

mstoldegon · Answer

The best way to look at any problem involving angels of polygons (triangle, 4, 5, 6... sided) is to break them down into triangles, or at least polygons with fewer sides.
   Take your current example: STUVX is a Pentagon, of which the interior angles will total 540; STYX and TUVY are both 4 sided (sometimes referred to as a Quadrilateral - why not a Quadragon???) and their interior angles will total 360.
   With no further information about other angles, the lengths of sides, or whether angles STX and SXY are Right Angles (90 deg), one cannot solve for anything else than would you were given.
   That said, here are some rules (next block).

mstoldegon · Answer

(Open Study is still having trouble - wiped out my answer before I finished :(
   Rules for determining the angles, and possibly the lengths of the sides, of Triangles, or Polygons if they can be broken down into triangles.
1. A Right triangle has one angle that is 90 deg. No sides or angles have to be equal to any other side or angle to be a Right Triangle.
2. An Isosceles triangle has 2 sides of equal length and hence two angles that are equal.
3. A Scalene triangle has no sides that are equal and no angles that are equal. Note: a Right Triangle can be a Scalene Triangle if no sides are equal in length.
3. One can determine the third angle of ANY triangle if they know the other two angles, regardless of whether one knows any of the lengths of the sides. The lengths are not bound to the value of the angles until one or more lengths is known.
4. One cannot determine the length of the third side of a triangle if they know 'just' the length of two of the sides (i.e. they don't know any of the angles) - Exception: If the lengths of the two adjacent sides of a Right triangle are known (the two sides that come together at the 90 deg angle), then the length of the opposite side (the Hypotenuse) can be determined, as well as the remaining angles.
5. The remaining angles and lengths of the sides can be determined if one knows the following about any triangle:
  a. The lengths of two sides and the angle between those sides.
  b. The lengths of two sides and any two of the three angles, no matter which ones they are.
  c. The length of one side and any two of the three angles, no matter which ones they are.
  Does this help?

anonymous · Answer

yes im still a bit confused but i get it much more than i did before thanks!