Question

The sum of the measures of two exterior angles of a triangle is 255. What is the measure of the third exterior angle?

Answer 1

For regular polygons where n = the number of sides:

Measure of one internal angle = 180°(1 - (2/n))
Sum of internal angles (for all polygons, not just regular) = 180°(n - 2)
Measure of one exterior angle = 360°/n
Sum of exterior angles (for all polygons, not just regular) = 360°

(a) The sum of the measures of exterior angles has to add up to 360°, so if we let the measure of the third exterior angle be x we can write

x + 255° = 360°
x = 360° - 255°
x = 105°

(b) Interior angle:
180°(1 - (2/n)) = 180°(1 - (2/6)) = 120°

Exterior angle:
360°/n = 360°/6 = 60°

Answer 2

Thank you!

Answer 3

No problem! :)