Answer
4) x = 7
5)
Step-by-step explanation
4) We are told that points M, N and P are on the same line (collinear). This means that
MN + NP = MP
We are then told further that
MN = 3x - 9
NP = x + 1
MP = 6x - 22
We can then make the necessary substitution
MN + NP = MP
(3x - 9) + (x + 1) = (6x - 22)
3x + x - 9 + 1 = 6x - 22
4x - 8 = 6x - 22
We can rewrite this as
6x - 22 = 4x - 8
6x - 4x = 22 - 8
2x = 14
Divide both sides by 2
(2x/2) = (14/2)
x = 7
5) We are asked to determine if point N is the midpoint of MP.
To do this, we would just compute the length of MN and NP and see if they are equal. If they are, then N is the midpoint of MP
MN = 3x - 9
MN = 3(7) - 9 = 21 - 9 = 12
NP = x + 1 = 7 + 1 = 8
MN ≠ NP since 12 ≠ 8
Hence, N is not the midpoint of MP.
6) From the description, we can tell that
Angle EBC = Angle EBD + Angle CBD
140° = Angle EBD + 35°
Angle EBD = 140° - 35° = 105°
Also, we can see that Angle EBC and Angle ABE sum up to give 180°
Angle EBC + Angle ABE = 180°
140° + Angle ABE = 180°
Angle ABE = 180° - 140° = 40°
b) BE is not perpendicular to BD.
Hope this Helps!!!