Questions: Three squares are joined together at the corners onto two vertical poles as shown. What is the value of x when the angles as shown? (A) 39° (B) 41° (C) 43° (D) 44° (E) 46°

Three squares are joined together at the corners onto two vertical poles as shown. What is the value of x when the angles as shown? (A) 39° (B) 41° (C) 43° (D) 44° (E) 46°
Transcript text: Three squares are joined together at the corners onto two vertical poles as shown. What is the value of $x$ when the angles as shown? (A) $39^{\circ}$ (B) $41^{\circ}$ (C) $43^{\circ}$ (D) $44^{\circ}$ (E) $46^{\circ}$
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Solution

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Solution Steps

Step 1: Identify Given Angles and Relationships
  • The problem involves three squares joined together at the corners.
  • Given angles are 30°, 124°, 75°, and 90°.
  • We need to find the value of angle x.
Step 2: Analyze the Geometry of the Squares
  • Each square has internal angles of 90°.
  • The angles at the corners where the squares meet will sum up to 360°.
Step 3: Set Up the Equation
  • The sum of the angles around point D (where the squares meet) is 360°.
  • The given angles around point D are 30°, 124°, 75°, and x.
  • Therefore, the equation is: 30° + 124° + 75° + x = 360°.
Step 4: Solve for x
  • Combine the given angles: 30° + 124° + 75° = 229°.
  • Subtract the sum from 360° to find x: 360° - 229° = 131°.

Final Answer

The value of x is 131°.

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