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Angles around a point, volume of a cuboid, and trigonometry problem. Find x, the volume, and angle theta.

Mathematics

ScanSolve AI Answer

Answer

C. 36∘\text{C. } 36^\circ

D. 36 cm3\text{D. } 36 \text{ cm}^3

Step-by-step solution

7 steps

53)

  1. Identify the relationship between the angles.

    The angles xx, 2x2x, 3x3x, and 4x4x are angles around a point. The sum of angles around a point is 360∘360^\circ.

  2. Set up the equation.

    x+2x+3x+4x=360∘x + 2x + 3x + 4x = 360^\circ
  3. Combine like terms.

    10x=360∘10x = 360^\circ
  4. Solve for xx.

    x=360∘10x = \frac{360^\circ}{10} x=36∘x = 36^\circ

    The value of xx is C. 36∘\boxed{\text{C. } 36^\circ}.

    54)

  5. Recall the formula for the volume of a cuboid.

    The volume VV of a cuboid is given by the formula:

    V=length×width×heightV = \text{length} \times \text{width} \times \text{height}
  6. Substitute the given values into the formula.

    Given: length = 6 cm, width = 3 cm, height = 2 cm.

    V=6 cm×3 cm×2 cmV = 6 \text{ cm} \times 3 \text{ cm} \times 2 \text{ cm}
  7. Calculate the volume.

    V=18 cm2×2 cmV = 18 \text{ cm}^2 \times 2 \text{ cm} V=36 cm3V = 36 \text{ cm}^3

    The volume of the cuboid is D. 36 cm3\boxed{\text{D. } 36 \text{ cm}^3}.

    55)
    To find the angle θ\theta in a right-angled triangle, at least two side lengths or one side length and another angle (besides the right angle) must be known. In the provided diagram, only one side length (6 cm) is given, which is opposite to angle θ\theta. The length of the adjacent side or the hypotenuse is not provided. Therefore, there is insufficient information to determine the value of θ\theta.

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