Question

Interior and Exterior Angle Sum of Polygon: Find a and b

Answer 1

The diagram shows a hexagon with unequal sides and angles. Two of the angles have been marked as 90 degrees, 116 degrees and 97 degrees. The side with the exterior angle measuring 83 degrees has the angle at that point measuring

Angle a = 180 - 83

Angle a = 97

Note that the sum of the internal angles of a hexagon is derived as;

S = 180 (n - 2)

S = 180 (6 - 2)

S = 180 x 4

S = 720

The remaining three angles added to the given and calculated angles all sum up to 720. That is;

`\begin{gathered} 90+116+97+y=720 \\ 303+y=720 \\ y=720-303 \\ y=417 \end{gathered}`

Observe that the other three angles are all equal, because the external angle for each of them, the ones marked x, are all equal as well. Hence, the other three external angles are derived as y divided by 3. That is 417 divided by 3 and that equals 139.

Angle b is one of these other three angles. Therefore angle b is 139 degrees.

Angle a is calculated as

Angle a = 180 - 116

Angle a = 64