Answer:
Explanation:
9) EFGH is a parallelogram. In a parallelogram, consecutive angles are supplementary. It means that the sum of the consecutive angles is 180 degrees.
Therefore,
16x - 2 + 8x + 14 = 180
16x + 8x = 180 - 14 + 2
24x = 168
x = 168/24
x = 7
Angle E = 8x + 14 = 8 × 7 + 14
Angle E = 56 + 14 = 70 degrees
b) consecutive angles are supplementary.
10) it is given that JM is parallel to KL.
Given that x = 3,
JM = 5x - 1 = 5 × 3 - 1 = 14
KL = 3x + 5 = 3 × 3 + 5 = 14
Since JM and KL are parallel and equal, then JK and ML is also equal and parallel. Therefore,
The quadrilateral is a parallelogram.
b) The opposite sides of a parallelogram are equal and parallel.
11) x = 7
y = 14
J = 9y + 1 = 9 × 14 + 1
J = 127 degrees
L = 10y - 13 = 10 × 14 - 13
L = 127 degrees
K = 7x + 4 = 7 × 7 + 4
K = 53 degrees
M = 360 - (127 + 127 + 53) = 360 - 307
M = 360 - 307 = 53 degrees
It is a parallelogram because
J = L and M = K
b) The opposite angles of a parallelogram are congruent. The consecutive angles of the parallelogram are supplementary. The sum of the angles in a parallelogram is 360 degrees