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The sum of 8 exterior angles of a decagon is 310°. The remaining two angles are equal. Find the size of each angle.

User Grorel
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Final Answer:

The size of each exterior angle of the decagon is 36°.

Step-by-step explanation:

The sum of exterior angles of any polygon is always 360°.

For a decagon, there are 10 exterior angles.

The sum of the 8 known exterior angles is 310°, leaving 360° - 310° = 50° for the remaining 2 angles.

Since the remaining two angles are equal, each of them is 50° / 2 = 25°.

Therefore, each exterior angle of the decagon is 360° / 10 = 36°.

The size of each exterior angle is 36°, and the equal remaining angles are 25° each, totaling 36° + 25° = 61°.

However, the question specifically asks for the size of each exterior angle, which is 36°.

User Mfurseman
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