Question

Find the measure of each exterior angle of the regular polygon.

Answer 1

Exterior Angle 1 (2x-10): 140 degrees

Exterior Angle 2 (x+25): 130 degrees

Exterior Angle 3 (right angle): 90 degrees

Explanation:

Givens:

Angle 3 = 90 degrees

Angle 1 + Angle 2 + Angle 3 = 180 degrees

Angle 1/2/3 + exterior angle = 180 degrees -> 180 - Angle1/2/3 = exterior angle

Step 1: Solving for x.

1. Using the first equation above, substitute the angles.

(2x-10) + (x+25) + 90 = 180

2. Combine like terms.

3x + 105 = 180

3. Solve for x.

3x = 75

x = 25

Step 2: Solving for angle 1 and 2.

Plug 25 in for x for both angles

Angle 1:

(2(25)-10) = 40 degrees

Angle 2:

((25)+25) = 50 degrees

Step 3: Solving for exterior angles.

Plug in the knowns to the second equation above and solve.

Angle 1:

180 - 40 = 140 degrees

Angle 2:

180 - 50 = 130 degrees

Angle 3:

180 - 90 = 90 degrees

I hope this helps!

Answer 2

x=25

Explanation:

90+2x-1-+x+25=180

3x+105=180

-105 -105

3x/3=25/3

Meaning x=25