I really need help, Ive been working on this forever, I know it's a rhombus but I need the measurements, I got 31 and I got 39

Question

anonymous · Answer

pic

whpalmer4 · Answer

Which measurements do you need?  The angles 1, 2, 3, 4?  Look at your diagram — isn't that a pair of identical triangles, with a known angle between two identical sides?  What does that imply about those angles?

anonymous · Answer

yes all numbered angles, I'm just not getting it

whpalmer4 · Answer

Ignore the top of the rhombus, just look at the triangle with angle 116 degrees and two identical sides.  What kind of triangle is that?  Do we know anything about the sum of the interior angles of a triangle?

anonymous · Answer

so 29

anonymous · Answer

no 58

whpalmer4 · Answer

Well, we know the 2 angles + 116 = 180, and the angles must be identical because this is an isosceles triangle and we know the angle in the middle.  if x is the angle, 2x + 116 = 180 and 2x = 180-116 = 64 and x = 32, right?  And the triangle on the other side is an identical triangle because all of the sides are the same length as the corresponding sides on this triangle, so the angles there must also be the same.