This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions to the problems: 6. Define the term polygon. Give two examples of polygons. A polygon is a closed two-dimensional shape made up of straight line segments connected end-to-end. Examples: Triangle, Square. 7. Find the measure of each interior angle of a regular hexagon. Step 1: Identify the number of sides for a hexagon. A hexagon has n=6 sides. Step 2: Use the formula for the measure of each interior angle of a regular polygon. The formula is ((n-2) × 180^)/(n). Step 3: Substitute n=6 into the formula and calculate. Interior Angle = ((6-2) × 180^)/(6) Interior Angle = (4 × 180^)/(6) Interior Angle = (720^)/(6) Interior Angle = 120^ 8. A polygon has an interior angle sum of 1260^. Calculate the number of sides it has. Step 1: Use the formula for the sum of interior angles of a polygon. The formula is (n-2) × 180^. Step 2: Set the formula equal to the given sum and solve for n. (n-2) × 180^ = 1260^ n-2 = (1260)/(180) n-2 = 7 n = 7 + 2 n = 9 9. One angle of a regular polygon measures 150^. Find the number of sides. Step 1: Use the formula for one interior angle of a regular polygon. The formula is ((n-2) × 180^)/(n). Step 2: Set the formula equal to the given angle and solve for n. ((n-2) × 180^)/(n) = 150^ (n-2) × 180 = 150n 180n - 360 = 150n 180n - 150n = 360 30n = 360 n = (360)/(30) n = 12 10. Draw a regular Octagon. I cannot provide a visual drawing. However, a regular octagon is a polygon with 8 equal sides and 8 equal interior angles. Each interior angle of a regular octagon measures 135^.