Answer:
The sixth angle of the hexagon is [tex]54^{o}[/tex].
Step-by-step explanation:
A convex hexagon is one that does not have equal length of sides i.e it is irregular.
Sum of angles in a polygon = (n - 2) x 180
For an hexagon, n = 6.
Sum of angles in a hexagon = (6 - 2) x 180
= 4 x 180
= [tex]720^{o}[/tex]
Therefore, let the sixth angle be represented by x, so that;
[tex]140^{o}[/tex] + [tex]140^{o}[/tex] + [tex]140^{o}[/tex] + [tex]84^{o}[/tex] + 3x + x = [tex]720^{o}[/tex]
[tex]504^{o}[/tex] + 4x = [tex]720^{o}[/tex]
4x = [tex]720^{o}[/tex] - [tex]504^{o}[/tex]
= [tex]216^{o}[/tex]
x = [tex]\frac{216}{4}[/tex]
= [tex]54^{o}[/tex]
The sixth angle of the hexagon is [tex]54^{o}[/tex].
Fifth angle = 3 x [tex]54^{o}[/tex]
= [tex]162^{o}[/tex]
