The measure of the sixth exterior angle of the hexagon will be 32°.
It is because sum of exterior angles of a closed polygon is 360°.
Given that:
- A convex hexagon is there.
- Its five of six exterior angles' measures are 80°, 68°, 84°, 56°, and 40°.
To find:
The remaining sixth exterior angle of the given hexagon.
Calculations for sixth exterior angle:
The sum of all exterior angles of any closed polygon is 360°.
Let the sixth angle of the given hexagon be s°. Then we will have:
[tex]80 + 68 + 84 + 56 + 40 + s = 360\\s + 328 = 360\\s = 360 - 328 = 32^\circ[/tex]
Thus, the measure of the sixth exterior angle of the hexagon will be 32°.
Learn more about exterior angles here:
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