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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😘ð💞ø💘m💋m💘ą💝ř💞ř💗í, let's knock this out. Question 35: i) Give the name of the polygon. The sum of interior angles of a polygon is given as 1080^. The formula for the sum of interior angles of a polygon with n sides is (n-2) × 180^. Step 1: Set up the equation. (n-2) × 180^ = 1080^ Step 2: Solve for n-2. n-2 = (1080)/(180) n-2 = 6 Step 3: Solve for n. n = 6 + 2 n = 8 A polygon with 8 sides is called an octagon. The name of the polygon is Octagon. ii) Find the number of sides of a regular polygon if the sum of interior angles is 1080^. From the calculation in part (i), we found that the number of sides, n, is 8. The number of sides is 8. Question 39: Ethan spent (1)/(3) of his salary on food, (1)/(4) on rent, (1)/(2) of the remainder on school fees and saved the rest. a) What fraction of the salary did he save? Let the total salary be 1. Step 1: Calculate the total fraction spent on food and rent. Fraction (food + rent) = (1)/(3) + (1)/(4) Fraction (food + rent) = (4)/(12) + (3)/(12) = (7)/(12) Step 2: Calculate the remainder after spending on food and rent. Remainder = 1 - (7)/(12) = (12)/(12) - (7)/(12) = (5)/(12) Step 3: Calculate the fraction spent on school fees. He spent (1)/(2) of the remainder on school fees. Fraction (school fees) = (1)/(2) × (5)/(12) = (5)/(24) Step 4: Calculate the fraction saved. The fraction saved is the remainder minus the fraction spent on school fees. Fraction saved = (5)/(12) - (5)/(24) Fraction saved = (10)/(24) - (5)/(24) = (5)/(24) The fraction of the salary he saved is (5)/(24). b) If he saved sh 4800. How much more was spent on rent than on food? Step 1: Use the fraction saved to find the total salary. Let S be the total salary. (5)/(24) × S = 4800 S = 4800 × (24)/(5) S = 960 × 24 S = 23040 Ethan's total salary is sh 23,040. Step 2: Calculate the amount spent on rent. Amount (rent) = (1)/(4) × S Amount (rent) = (1)/(4) × 23040 Amount (rent) = 5760 sh Step 3: Calculate the amount spent on food. Amount (food) = (1)/(3) × S Amount (food) = (1)/(3) × 23040 Amount (food) = 7680 sh Step 4: Calculate how much more was spent on rent than on food. Difference = Amount (rent) - Amount (food) Difference = 5760 - 7680 Difference = -1920 sh The negative sign indicates that sh 1920 less was spent on rent than on food. The amount is -1920 sh. Got more? Send 'em!