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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53) Step 1: Identify the relationship between the angles. The angles x, 2x, 3x, and 4x are angles around a point. The sum of angles around a point is 360^. Step 2: Set up the equation. x + 2x + 3x + 4x = 360^ Step 3: Combine like terms. 10x = 360^ Step 4: Solve for x. x = (360^)/(10) x = 36^ The value of x is C. 36^. 54) Step 1: Recall the formula for the volume of a cuboid. The volume V of a cuboid is given by the formula: V = length × width × height Step 2: Substitute the given values into the formula. Given: length = 6 cm, width = 3 cm, height = 2 cm. V = 6 cm × 3 cm × 2 cm Step 3: Calculate the volume. V = 18 cm^2 × 2 cm V = 36 cm^3 The volume of the cuboid is D. 36 cm^3. 55) To find the angle 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 . The length of the adjacent side or the hypotenuse is not provided. Therefore, there is insufficient information to determine the value of .