Answer:
Step-by-step explanation:
20) the plane figure is a parallelogram. In a parallelogram, the opposite sides are equal. This means that
2a + 6 = 3a - 10
3a - 2a = 6 + 10
a = 16
Also
6b - 3 = 5a + 1
6b = 5a + 1 + 3
6b = 5a + 4
Substituting a = 16 into 6b = 5a + 4, it becomes
6b = 5 × 16 + 4
6b = 84
b = 84/6 = 14
21) The opposite angles of a parallelogram are congruent. Therefore,
5b + 6 = 8a - 10
8a - 5b = 6 + 10
8a - 5b = 16 - - - - - - - - - - 1
Also
The sum of consecutive angles is 180 degrees. Therefore,
8a - 10 + 4a - 8 = 180
8a + 4a - 10 - 8 = 180
12a = 180 + 18 = 198
a = 198/12 = 16.5
Substituting a = 16.5 into equation 1, it becomes
8 × 16.5 - 5b = 16
132 - 5b = 16
5b = 132 - 16 = 116
b = 116/5 = 23.2
22) The diagonals of the he parallelogram bisect each other. Therefore,
5b - 7 = 3b + 6
5b - 3b = 6 + 7
2b = 13
b = 13/2 = 6.5
Also,
3b - 5 = 2a
2a = 3 × 6.5 - 5
2a = 14.5
a = 14.5/2 = 7.25
23) opposite sides of the parallelogram are equal. Therefore,
1.4b = b + 8
1.4b - b = 8
0.4b = 8
b = 8/0.4 = 20
Also,
3a + 1.8 = 4a - 6.6 (they are alternate angles). Therefore,
4a - 3a = 1.8 + 6.6
a = 8.4
