Four of the angles of a hexagon measure 53°, 126°, 89°, and 117°. What is the sum of the measures of the other two angles?
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To find the sum of the measures of the other two angles of a hexagon, we need to know that the sum of interior angles in any polygon is given by the formula (n-2) * 180 degrees, where n is the number of sides of the polygon.
Since a hexagon has six sides, we can find the sum of the interior angles by substituting 6 into the formula:
Sum of interior angles = (6 - 2) * 180 degrees
= 4 * 180 degrees
= 720 degrees
Now, we know that the sum of all six angles is equal to 720 degrees.
To find the sum of the measures of the other two angles, we subtract the sum of the given four angles from the sum of all six angles:
Sum of the other two angles = Sum of all six angles - Sum of the given four angles
= 720 degrees - (53 degrees + 126 degrees + 89 degrees + 117 degrees)
= 720 degrees - 385 degrees
= 335 degrees
Therefore, the sum of the measures of the other two angles is 335 degrees.