Question

Cals 1/2

10. MA bisects segment CB at midpoint M. Based on the definition of angle bisector and midpoint, find the value
of x and the following measures.
Middle
x =
MB.=
CM =
CB =
x+6
(92)
M
2r-4
B

Answer 1

• x = 10
• MB = 16
• CM = 16
• CB = 32

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