Question

34. The measures of the exterior angles of a convex

pentagon can be represented as follows: m/1 = x, m/2=2x+5, m≤3 = 3x + 6, m/4 = 5x + 13, m/5=5x+16. Find the measure of each angle.
m/1= _________________ degrees
m/2=_________________ degrees
m/3 =_________________ degrees
m/4= _________________ degrees
m_5 = _________________ degrees

Answer 1

20° , 45° , 66° , 113° , 116°

Explanation:

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

sum the 5 angles and equate to 360

x + 2x + 5 + 3x + 6 + 5x + 13 + 5x + 16 = 360

16x + 40 = 360 ( subtract 40 from both sides )

16x = 320 ( divide both sides by 16 )

x = 20

Then substitute x = 20 into each of the given angle measures

∠ 1 = x = 20°

∠ 2 = 2x + 5 = 2(20) + 5 = 40 + 5 = 45°

∠ 3 = 3x + 6 = 3(20) + 6 = 60 + 6 = 66°

∠ 4 = 5x + 13 = 5(20) + 13 = 100 + 13 = 113°

∠ 5 = 5x + 16 = 5(20) + 16 = 100 + 16 = 116°