Question - Calculating Interior Angles of a Hexagon
Solution:
The diagram provided is of a hexagon, which has six sides. The sum of the interior angles of a hexagon can be calculated using the formula:Sum of interior angles = (n - 2) × 180°where n is the number of sides in the polygon. For a hexagon, n = 6.So the sum of the interior angles of our hexagon will be:(6 - 2) × 180° = 4 × 180° = 720°From the image, we can see three interior angles are shown. Two of them have the measures of 120° and 135°, and the third angle is labeled as x. We also know that the remaining three interior angles are equal, which means each one has the same measure as x.Since the sum of all the interior angles is 720°, we can set up the following equation:120° + 135° + x + x + x + x = 720°Now, we combine the known angles and the x's:255° + 4x = 720°Subtracting 255° from both sides gives us:4x = 720° - 255°4x = 465°Finally, we solve for x by dividing both sides by 4:x = 465° ÷ 4x = 116.25°So, each of the remaining three interior angles, including the one labeled as x in the diagram, measures 116.25°.
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