Question

Given a ∆ with exterior angles (55x)°, (40x)°, (85x)°

a. Find the measure of the largest exterior angle.

b. Find the measure of the smallest interior angle.

Answer 1

Part A : 170

Part B: 10

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