Answer:
Step-by-step explanation:
10) The opposite sides of a parallelogram are equal. It means that
a + 15 = 3a + 11
3a - a = 15 - 11
2a = 4
a = 4/2 = 2
Also,
3b + 5 = b + 11
3b - b = 11 - 5
2b = 4
b = 4/2 = 2
11) The opposite angles of a parallelogram are congruent and the adjacent angles are supplementary. This means that
2x + 11 + x - 5 = 180
3x + 6 = 180
3x = 180 - 6 = 174
x = 174/3 = 58
Therefore,
2x + 11 = 2×58 + 11 = 127 degrees
The opposite angles of a parallelogram are congruent, therefore,
2y = 127
y = 127/2 = 63.5
12) The diagonals of a parallelogram bisect each other. This means that each diagonal is divided equally at the midpoint. Therefore
3y - 5 = y + 5
3y - y = 5 + 5
2y = 10
y = 10/2 = 5
Also,
z + 9 = 2z + 7
2z - z = 9 - 7
z = 2
