The diagram shows part of a regular polygon. work out how many sides the polygon has. (it is 156 degrees).
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To determine the number of sides in a regular polygon given an interior angle, you can use the formula:
n = 360 / A,
where n represents the number of sides and A represents the measure of the interior angle of the regular polygon.
In this case, we know the interior angle is 156 degrees. Plugging this value into the formula, we get:
n = 360 / 156,
Evaluating the expression gives:
n ≈ 2.308,
Since the number of sides must be a whole number for a regular polygon, we need to round the result to the nearest whole number. By rounding to the nearest whole number, we find that the polygon has 2 sides.
However, it is important to note that a regular polygon cannot have fewer than 3 sides. Therefore, if we encounter a situation where the rounded result is less than 3, we know that the given angle does not correspond to a regular polygon. In this case, the given angle of 156 degrees does not represent a valid regular polygon.