Answer:
Explanation:
Given M is the midpoint of GQ with MG = 5x+8 and GQ = 6x+56, you want the value of x, and the measures of MQ and GQ.
Midpoint
The midpoint divides the segment GQ into two congruent parts, each of which is half the length of GQ.
GQ = 2·MG
6x +56 = 2(5x +8)
6x +56 = 10x +16 . . . . . . eliminate parentheses
40 = 4x . . . . . . . . . . . subtract 6x+16
10 = x . . . . . . . . . divide by 4
Segments
Using the found value of x, we see the segment lengths are ...
MG = 5(10) +8 = 58
GQ = 6(10) +56 = 116
MQ = GQ -MG = 116 -58 = 58
The value of x is 10, and the lengths are MQ = 58 and GQ = 116.
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