find the value of x, y, and z in the parallelogram below.
find the value of x, y, and z in the parallelogram below.
Answer
Explanation:
Step1: Use opposite - angle property
In a parallelogram, opposite angles are equal. So, (3y + 6=111). [3y+6 = 111] [3y=111 - 6] [3y = 105] [y=\frac{105}{3}=35]
Step2: Use adjacent - angle property
Adjacent angles in a parallelogram are supplementary (sum to (180^{\circ})). So, ((-6x - 3)+111 = 180). [-6x-3+111 = 180] [-6x+108 = 180] [-6x=180 - 108] [-6x = 72] [x=- 12]
Step3: Use opposite - angle property again
Since opposite angles are equal, (5z + 4=111). [5z+4 = 111] [5z=111 - 4] [5z = 107] [z=\frac{107}{5}=21.4]
Answer:
(x=-12), (y = 35), (z = 21.4)