1. What is the sum of the interior anglesof a hexagon?2. How many sides does a regularpolygon have if each interior anglemeasures 140°?3. Find the measure of each exteriorangle of a regular dodecagon.please po pakisagutan po
Answer (1)
Answer:Let's solve each of the geometry problems step by step: 1. Sum of Interior Angles of a Hexagon:The sum of the interior angles of a polygon can be calculated using the formula: where is the number of sides of the polygon. For a hexagon (a polygon with 6 sides): Therefore, the sum of the interior angles of a hexagon is .2. Number of Sides of a Regular Polygon with 140° Interior Angle:For a regular polygon, all interior angles are equal. Let's denote the measure of each interior angle as .Since each interior angle measures 140°, we have: The formula to calculate the interior angle of a regular polygon is: where is the number of sides. Substituting into the formula: Therefore, a regular polygon with each interior angle measuring 140° has 9 sides.3. Measure of Each Exterior Angle of a Regular Dodecagon:For a regular polygon, the sum of the exterior angles is always 360°. The formula to calculate the measure of each exterior angle is: where is the number of sides. For a regular dodecagon (a polygon with 12 sides): Therefore, the measure of each exterior angle of a regular dodecagon is .
