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5 votes
In the polygon pictured, which angles are supplementary?

1) c° and i°
2) g° and f°
3) a° and k°
4) c° and d°

User Tdon
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1 Answer

4 votes

Final Answer:

The angles that are supplementary in the given polygon is c° and d°, thus the correct option is 4.

Step-by-step explanation:

Supplementary angles are those whose measures sum up to 180 degrees. In the polygon provided, angles c° and d° are adjacent angles sharing a common side, forming a straight line. When two angles form a straight line, they create a linear pair and are thus supplementary. In this case, as both angles c° and d° together form a straight line within the polygon, their measures add up to 180 degrees.

This is evident from the fact that the interior angles of a polygon with n sides sum up to (n-2) * 180°. In this case, considering it's a polygon, the sum of its interior angles would be (10 - 2) * 180° = 8 * 180° = 1440°. As there are ten angles in the polygon, each angle's average measure is 1440° / 10 = 144°. Therefore, the angles that are supplementary, i.e., angles c° and d°, are supplementary, forming a linear pair, and their measures sum up to 180 degrees, as demonstrated by their positioning within the polygon. Hence, option 4) c° and d° are supplementary angles within the given polygon.

In the polygon pictured, which angles are supplementary? 1) c° and i° 2) g° and f-example-1
User Juned Ahsan
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