Sides of a Polygon GivenSum of theDivide the AnglePolygonAnglemeasuresSum by 180°AngleAdd 2 to thequotient of AngleSum divided by180°Number of Sides giventhe Angle Sum180°Triangle180°11+2+2=1+2180°= 3360°+2=2+2Quadrilateral360°22+2180°= 4PentagonHexagonHeptagonOctagonNonagonDecagonHendecagonDodecagonn-gonTasks/Questions: Answer the questions below.1) What pattern did you observe?2) Write your generalization on how to find the number of sides given the sum of the measures ofangles of a convex polygon.(Need for monday po..)​

Divide the Angle Sum by 180°: This step essentially tells us how many sets of 180° angles are contained within the polygon's total angle sum.Add 2: Adding 2 to the result accounts for the fact that a triangle (3 sides) has an angle sum of 180°, a quadrilateral (4 sides) has an angle sum of 360° (two sets of 180°), and so on.Example:If the sum of the interior angles of a polygon is 1080°, we can find the number of sides:n = (1080° / 180°) + 2n = 6 + 2n = 8Therefore, the polygon has 8 sides (an octagon).In Summary:The formula n = (S / 180°) + 2 provides a direct and efficient way to determine the number of sides of a convex polygon given the sum of its interior angles.Step-by-step explanation:

Answered by terenzwilliam | 2024-09-07