Question

Find the value of x, y, and z in the parallelogram below. x (4y+5)°, y (-8z-7)°, z (3x-8)°

Answer 1

I don’t have the diagram, so I’m not certain which angle each expression labels (which angles are opposite or adjacent). Could you either upload the picture or say which expressions sit at which corners of the parallelogram?

If you meant the three given expressions label three consecutive angles around the parallelogram (say top-left = (4y+5)°, top-right = (−8z−7)°, bottom-right = (3x−8)°), then the parallelogram relations give

- opposite angles equal: (4y+5) = (3x−8) -> 3x − 4y = 13
- adjacent angles supplementary: (4y+5) + (−8z−7) = 180 -> 4y − 8z = 182

(the other adjacency equation is then the same as these). These two independent linear equations leave one free parameter, so x,y,z are not uniquely determined from that information alone. Solving gives

x = (4y + 13)/3, z = (2y − 91)/4,

with y free (subject to angle-range constraints if you require 0°<angles<180° or integrality).

If instead the three expressions correspond to the numeric values x, y, z (i.e. x = 4y+5, y = −8z−7, z = 3x−8) please confirm and I will solve that system.

Tell me which diagram/assignment is correct (or upload the picture) and I’ll finish the solution.