Answer:
- x = 10
- MB = 16
- CM = 16
- CB = 32
Step-by-step explanation:
There are two different relations here that can be used to write equations for the value of x:
- a perpendicular to a line creates a linear pair of right angles
- a midpoint divides a segment into two congruent segments
Value of x
Using the angle relation, we have ...
∠CMA ≅ ∠BMA
(9x)° = 90°
x = 90/9 = 10
Segment lengths
Using the found value of x in the expressions for the segment lengths, we find ...
MB = 2x -4 = 2(10) -4 = 16
CM = x +6 = 10 +6 = 16 . . . . . . . congruent to MB, as it should be
CB = CM +MB = 16 +16 = 32
