Answer:
Part A : 170
Part B: 10
Step-by-step explanation:
In any convex polygon, the exterior angles add to 360 degrees.
55x + 40x + 85x = 360 Combine the left side
180x = 360 Divide by 180
180x/180 = 360/180
x = 2
Part A
The largest exterior angle is going to be 85x = 85*2 = 170 degrees.
Part B
The exterior and interior angles are supplementary. That is they add up to 180 degrees.
The smallest one is going to be with the 85x angle. That angle eats up a lot of real estate.
Let y = the interior angle. Set up the equation
85x + y = 180 Solve for 85x
170 + y = 180 Subtract 170 from both sides
170 - 170 + y = 180 - 170
y = 10 degrees
