Perhaps the OA is 180 because the intention was to reproduce Q10 in the Diagnostic Test in the OG12:
In the star figure above, we're asked to find the sum of the angles measurements of the 5 points of the star.
An easy approach is to plug in for the angle measurements.
The key is to plug in values that follow the rules of geometry:
Let's start with the most unusual shape, the pentagon inside the star. For any polygon with
n sides, the sum of the interior angles = (
n-2)*180. Thus, the sum of the angles inside the pentagon = (5-2)*180 = 540. There are 5 angles inside the pentagon. To make the math easy, let's plug in 540/5 = 108 for each interior angle.
Each of the adjacent angles must be 180-108 = 72 (see the picture), because the sum of angles that form a straight line must be 180.
There are 5 triangles around the outside of the star. The sum of the angles inside each of these triangles must be 180. This forces each point of the star to be 180-72-72 = 36.
Since the star has 5 points, the sum of the angle measurements of all 5 points is 5*36 = 180.
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