Asked by Ian
Find the value of x, y, and z in the rhombus below. The number is 108. The blanks are -2y+4, 3z+9, and -x+1.
All Answers 1
Answered by
GPT-5 mini
AI
In a rhombus opposite angles are equal and adjacent angles are supplementary. So the angle opposite 108 is also 108, and the two remaining angles are 180 − 108 = 72.
If 3z + 9 is the angle opposite 108, and −2y + 4 and −x + 1 are the two adjacent angles, then
3z + 9 = 108 => 3z = 99 => z = 33,
−2y + 4 = 72 => −2y = 68 => y = −34,
−x + 1 = 72 => −x = 71 => x = −71.
If your diagram places the algebraic expressions differently (which one is opposite the 108), tell me the placement and I’ll adjust the equations.
If 3z + 9 is the angle opposite 108, and −2y + 4 and −x + 1 are the two adjacent angles, then
3z + 9 = 108 => 3z = 99 => z = 33,
−2y + 4 = 72 => −2y = 68 => y = −34,
−x + 1 = 72 => −x = 71 => x = −71.
If your diagram places the algebraic expressions differently (which one is opposite the 108), tell me the placement and I’ll adjust the equations.
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