Question

The exterior angles of a pentagon are (m+5)°, (2m+3)°, (3m+2)°, (4m+1)° and (5m+4)° respectively. Find the measure of each angle. ​

Answer 1

see explanation

Explanation:

The sum of the exterior angles of a polygon = 360°

Sum the angles and equate to 360

m + 5 + 2m + 3 + 3m + 2 + 4m + 1 + 5m + 4 = 360, that is

15m + 15 = 360 ( subtract 15 from both sides )

15m = 345 ( divide both sides by 15 )

m = 23

Then

m + 5 = 23 + 5 = 28°

2m + 3 = 2(23) + 3 = 46 + 3 = 49°

3m + 2 = 3(23) + 2 = 69 + 2 = 71°

4m + 1 = 4(23) + 1 = 92 + 1 = 93°

5m + 4 = 5(23) + 4 = 115 + 4 = 119°

Answer 2

Explanation:

Sum of exterior angles of any polygon =360°

Sum of exterior angles of polygon = 360°

m + 5 + 2m + 3 + 3m + 2 + 4m + 1 + 5m + 4 = 360

m + 2m + 3m + 4m + 5m + 5 + 3 + 2 + 1 + 4 = 360 {Combine like terms}

15m + 15 = 360 {Subtract 15 from both sides}

15m = 360 - 15

15m = 345 {Divide both sides by 15}

m = 345/15

m = 23

m + 5 = 23 + 5 = 28°

2m + 3 = 2*23 + 3 = 46 + 3 = 49°

3m + 2 = 3*23 + 2 = 69 + 2 = 71°

4m + 1 = 4*23 + 1 = 92 + 1 = 93°

5m + 4 = 5*23 + 4 = 115 + 4 = 119°