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The sum of an interior angle and its corresponding exterior angle of any polygon is 180^.

Mathematics

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25) Exterior angle of a regular polygon is 72∘72^\circ. Calculate its interior angle.

  1. The sum of an interior angle and its corresponding exterior angle of any polygon is 180∘180^\circ.

    Interior angle+Exterior angle=180∘\text{Interior angle} + \text{Exterior angle} = 180^\circ

  2. Substitute the given exterior angle into the formula.

    Interior angle+72∘=180∘\text{Interior angle} + 72^\circ = 180^\circ

  3. Subtract the exterior angle from 180∘180^\circ to find the interior angle.

    Interior angle=180∘−72∘=108∘\text{Interior angle} = 180^\circ - 72^\circ = 108^\circ

    The interior angle is 108∘\boxed{\text{}108^\circ\text{}}

    26) Find the Highest Common Factor of numbers 30, 36 and 48.

  4. 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

  5. Identify the common factors.

    The common factors are 1, 2, 3, 6.

  6. Determine the highest common factor from the common factors.

    The highest common factor is 6.
    The Highest Common Factor is 6\boxed{\text{}6\text{}}

    27) Find the value of xx in the equation 3(x+1)=93(x+1)=9.

  7. Divide both sides of the equation by 3.

    3(x+1)3=93\frac{3(x+1)}{3} = \frac{9}{3} x+1=3x+1 = 3

  8. Subtract 1 from both sides to solve for xx.

    x=3−1x = 3 - 1 x=2x = 2

    The value of xx is 2\boxed{\text{}2\text{}}

    28) If 34\frac{3}{4} of the pupils in P6 class are girls, find the number of boys who are in class if there are 48 pupils.

  9. Calculate the number of girls in the class.

    Number of girls=34×48\text{Number of girls} = \frac{3}{4} \times 48 Number of girls=3×12=36\text{Number of girls} = 3 \times 12 = 36

  10. 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\text{Number of boys} = \text{Total pupils} - \text{Number of girls} Number of boys=48−36=12\text{Number of boys} = 48 - 36 = 12

    The number of boys in the class is 12\boxed{\text{}12\text{}}

    29) A circular garden has a radius of 15 cm. Find its area (π=3.14\pi = 3.14).

  11. Recall the formula for the area of a circle.

    A=πr2A = \pi r^2

  12. Substitute the given values for π\pi and the radius rr.

    A=3.14×(15 cm)2A = 3.14 \times (15 \text{ cm})^2 A=3.14×225 cm2A = 3.14 \times 225 \text{ cm}^2

  13. Calculate the area.

    A=706.5 cm2A = 706.5 \text{ cm}^2

    The area of the circular garden is 706.5 cm2\boxed{\text{}706.5 \text{ cm}^2\text{}}

    30) Find the volume of a cube whose sides are 7 dm. Give the answer in cm3^3.

  14. Convert the side length from decimeters (dm) to centimeters (cm).

    Since 1 dm = 10 cm,

    Side length=7 dm=7×10 cm=70 cm\text{Side length} = 7 \text{ dm} = 7 \times 10 \text{ cm} = 70 \text{ cm}

  15. Recall the formula for the volume of a cube.

    V=s3V = s^3

  16. Substitute the side length in centimeters into the formula and calculate the volume.

    V=(70 cm)3V = (70 \text{ cm})^3 V=70 cm×70 cm×70 cmV = 70 \text{ cm} \times 70 \text{ cm} \times 70 \text{ cm} V=343000 cm3V = 343000 \text{ cm}^3

    The volume of the cube is 343000 cm3\boxed{\text{}343000 \text{ cm}^3\text{}}

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