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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Hey Placide, good to see you again. 25) Exterior angle of a regular polygon is 72^. Calculate its interior angle. Step 1: The sum of an interior angle and its corresponding exterior angle of any polygon is 180^. Interior angle + Exterior angle = 180^ Step 2: Substitute the given exterior angle into the formula. Interior angle + 72^ = 180^ Step 3: Subtract the exterior angle from 180^ to find the interior angle. Interior angle = 180^ - 72^ = 108^ The interior angle is 108^ 26) Find the Highest Common Factor of numbers 30, 36 and 48. Step 1: List the factors for each number. • Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 • Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 • Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Step 2: Identify the common factors. The common factors are 1, 2, 3, 6. Step 3: Determine the highest common factor from the common factors. The highest common factor is 6. The Highest Common Factor is 6 27) Find the value of x in the equation 3(x+1)=9. Step 1: Divide both sides of the equation by 3. (3(x+1))/(3) = (9)/(3) x+1 = 3 Step 2: Subtract 1 from both sides to solve for x. x = 3 - 1 x = 2 The value of x is 2 28) If (3)/(4) of the pupils in P6 class are girls, find the number of boys who are in class if there are 48 pupils. Step 1: Calculate the number of girls in the class. Number of girls = (3)/(4) × 48 Number of girls = 3 × 12 = 36 Step 2: Subtract the number of girls from the total number of pupils to find the number of boys. Number of boys = Total pupils - Number of girls Number of boys = 48 - 36 = 12 The number of boys in the class is 12 29) A circular garden has a radius of 15 cm. Find its area ( = 3.14). Step 1: Recall the formula for the area of a circle. A = r^2 Step 2: Substitute the given values for and the radius r. A = 3.14 × (15 cm)^2 A = 3.14 × 225 cm^2 Step 3: Calculate the area. A = 706.5 cm^2 The area of the circular garden is 706.5 cm^2 30) Find the volume of a cube whose sides are 7 dm. Give the answer in cm^3. Step 1: Convert the side length from decimeters (dm) to centimeters (cm). Since 1 dm = 10 cm, Side length = 7 dm = 7 × 10 cm = 70 cm Step 2: Recall the formula for the volume of a cube. V = s^3 Step 3: Substitute the side length in centimeters into the formula and calculate the volume. V = (70 cm)^3 V = 70 cm × 70 cm × 70 cm V = 343000 cm^3 The volume of the cube is 343000 cm^3 Send me the next one 📸