Based on the following figure, determine which value below is correct.
The triangle A-B-C with angle B-C-A as left parenthesis 6-x plus 27 right parenthesis degrees. The triangle C-D-E with angle D-C-E as left parenthesis 12-x minus 9 right parenthesis degrees.
A.
x = 6
B
.
x = 9
C.
m∠ABC = 51°
D.
m∠ABC = 81°
C. m∠ABC = 51°
To solve this problem, we can use the fact that the sum of angles in a triangle is 180 degrees. So, we can set up an equation based on the information given:
Angle B-C-A + Angle D-C-E = 180 degrees
(6-x + 27) + (12-x - 9) = 180
6-x + 27 + 12-x - 9 = 180
39 - 2x = 180
-2x = 141
x = -70.5
Since x cannot be negative in this context, it is clear that m∠ABC = 6-x + 27 = 6-(-70.5) + 27 = 6 + 70.5 + 27 = 103.5 degrees
So, no value provided is correct, as x = 103.5.