Question

Find the value of x, y, and z in the rhombus below. The number is 98. the blanks are -y-5, -10x-8, and -2z+8.

Answer 1

I’m missing the picture, so I’ll give the solution for the most likely interpretation and also show other possibilities.

Most likely interpretation (the hyphens are just dashes; the expressions are y−5, 10x−8, 2z+8; 98 is one angle of the rhombus):
- In a rhombus opposite angles are equal and adjacent angles are supplementary. If one angle is 98°, the opposite is 98° and each adjacent angle is 180−98 = 82°.
- So y−5 = 98 → y = 103.
- 10x−8 = 82 → 10x = 90 → x = 9.
- 2z+8 = 82 → 2z = 74 → z = 37.

Answer (most likely): x = 9, y = 103, z = 37.

If instead the hyphens were minus signs (the expressions are −y−5, −10x−8, −2z+8) and those equal 98, then:
- −y−5 = 98 → y = −103
- −10x−8 = 98 → x = −53/5
- −2z+8 = 98 → z = −45

If the 98 referred to a side length (so each side = 98), set each expression equal to 98 and solve; that gives either (y, x, z) = (103, 53/5, 45) or the negative-case values above depending on whether the leading signs are minus signs or not.

If you can upload the picture or confirm whether the expressions are y−5, 10x−8, 2z+8 and whether 98 is an angle or a side, I’ll confirm which of the solutions is correct.