The question is incorrect. X is not defined UNLESS the hexagon is a regular hexagon, which means that all sides are equal (given) AND all angles are equal (not given).

Error in question aside, and ASSUMING the hexagon is regular, you can apply the principle that
1. the sum of exterior angles of ANY polygon is 360.
2. the sum of exterior angles and interior angles at EACH vertex is 180.
3. Multiply sum from (2) above by the number of vertices and subtract 360 gives the sum of the interior angles.
4. IF the polygon is regular (all angles equal), then each interior angle equals the result from (3) divided by n, the number of vertices.

Example for a regular heptagon (7 sides, 7 verfices).
1. Sum of exterior angles = 360
2. sum of interior and exterior angles at EACH vertex=180
3. multiply 180 by 7, subtract 360
180*7-360=900
4. since heptagon is regular, each interior angle equals 900/7=128.57 deg.

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3 years ago