Question

If three of the interior angles of a convex hexagon each measure 140, a fourth angle measures 84, and the

Answer 1

Answer:

The sixth angle of the hexagon is $54^{o}$.

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

                                               = $720^{o}$

Therefore, let the sixth angle be represented by x, so that;

$140^{o}$ + $140^{o}$ + $140^{o}$ + $84^{o}$ + 3x + x = $720^{o}$

$504^{o}$ + 4x = $720^{o}$

4x = $720^{o}$ - $504^{o}$

    = $216^{o}$

x = $\frac{216}{4}$

  = $54^{o}$

The sixth angle of the hexagon is $54^{o}$.

Fifth angle = 3 x $54^{o}$

                  = $162^{o}$