Answer:
Smallest to Largest: Angle ACD, Angle ADC, Angle CAD, Angle ACB
Step-by-step explanation:
To find the angles, let's first solve for x.
Let's call the missing side angle ACD= y
We know that there are 180 degrees in a triangle. So we can write the equation,
6x+4+(4x-2)+y= 180
and, We know that angle ACB is a linear pair with angle ACD, so both angles would add up to 180 degrees. We can write the equation,
9x+16+y=180
Let's now solve for x with both of these equations using elimination.
Simplify the equations,
6x+4+(4x-2)+y= 180 -> 10x+y=178
9x+16+y=180 -> 9x+y=164
-1(10x+y=178) -> -10x-y=-178
-10x-y=-178
9x+y=164
-x= -14
x= 14
Now that we have solved for x, we can find the missing angles.
Angle ACB= 9x+16 -> 9(14)+16= 142 degrees
Angle CAD= 6x+4 -> 6(14)+4= 88 degrees
Angle ADC= 4x-2 -> 4(14)-2= 54 degrees
Angle ACD= 180-(Angle CAD+ Angle ADC) -> 180-(88+54)= 38 degrees
