If three of the interior angles of a convex hexagon each measure 140, a fourth angle measures 84, and the measure of the fifth angle is 3 times the measure of the sixth angle, find the measure of the sixth angle.

The sixth angle of the hexagon is .

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

                                               =

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

+ + + + 3x + x =

+ 4x =

4x = -

    =

x =

  =

The sixth angle of the hexagon is .

Fifth angle = 3 x

                  =

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step-by-step explanation: