Question

Find the value of x, y, and z in the parallelogram 75° on the bottom right x (-7z+7)° on the top y (-y+9)° on the top left z (4x+1)° on the bottom

Answer 1

I’m not sure I’m reading the picture correctly. Could you confirm which angle expression is at each vertex? Please list the four vertices in order (for example: top-left, top-right, bottom-right, bottom-left) and give the angle at each one. For example:

- top-left = ?
- top-right = ?
- bottom-right = ?
- bottom-left = ?

From your text I see these expressions: 75°, x, (-7z+7)°, y, (-y+9)°, z, (4x+1)°. I need to know which four of those correspond to the four interior angles of the parallelogram.

If it helps, here’s how I’ll solve it once you give the mapping:
- Opposite angles of a parallelogram are equal (top-left = bottom-right, top-right = bottom-left).
- Adjacent angles are supplementary (sum to 180°).

So you’ll get equations like A = C and B = D, or A + B = 180°, etc., and I can solve that system for x, y, z. Send the vertex labeling and I’ll finish the work.