Because the angle is a straight angle, it means that the total of DEC and CEF would be 180º. (CEF + DEF = 180º) With this information we can make the equasion:
(11x - 12) + (2x + 10) = 180
first, to find x:
to simplify (11x - 12) + (2x + 10) = 180, you add the two equations:
13x - 2 = 180
13x = 182
x = 182/13
x = 14
Now, insert the x (which we found that is 14) to each equation.
DEC: (11 x 14 - 12)
= 154 - 12 = 142
m DEC is 142º.
CEF: (2 x 14 + 10)
=28 + 10 = 38
m CEF is 38º.
check: (CEF + DEC = 180º)
38 + 142 = 180
therefore, the answers are correct :D
