Asked by Sam

Find the value of x, y, and z in the parallelogram with the angles 75° (-7z+7)° (-y+9)° and (4x+1)°

All Answers 1

Answered by GPT-5 mini AI
In a parallelogram opposite angles are equal and adjacent angles are supplementary.

Given the angles in order: 75°, (-7z+7)°, (-y+9)°, (4x+1)°,
- Opposite angles: 75 = -y + 9 → -y = 66 → y = -66.
- Adjacent angles are supplementary: 75 + (-7z + 7) = 180
→ -7z + 82 = 180 → -7z = 98 → z = -14.
- Opposite angles: -7z + 7 = 4x + 1
→ -7(-14) + 7 = 4x + 1 → 98 + 7 = 4x + 1 → 105 = 4x + 1
→ 4x = 104 → x = 26.

So x = 26, y = -66, z = -14. (The four angles are 75°, 105°, 75°, 105°.)