Answer: The correct answer is option A: Line AB
Step-by-step explanation: The side opposite the widest/largest angle is the longest side, so we shall start by filling in the missing angles.
Looking at triangle DBC, two angles have already been identified which are angles 18 and 24. The third angle can be calculated as
B + 18 + 24 = 180 {Sum of angles in a triangle equals 180}
B + 42 = 180
Subtract 42 from both sides of the equation
B = 138
If Angle B is 138, looking at triangle ADB, angle B shall be derived as
B + 138 = 180 {Sum of angles on a straight line equals 180}
Subtract 138 from both sides of the equation
B = 42
If in triangle ADB we have identified angles 66 and 42, the third angle shall be calculated as follows
D + 66 + 42 = 180 {Sum of angles in a triangle equals 180}
D + 108 = 180
Subtract 108 from both sides of the equation
D = 72.
The largest angle in the triangle ABD is angle 72, therefore the longest side would be line AB (facing the angle 72)
