A draftsman needs to construct a precise 75° angle without using a protractor. Which combination of instruments should be used?
Use a 45° set-square with a 30°–60° set-square against a T-square
To construct a precise 75° angle without using a protractor, the correct combination of instruments would involve using a 45° set-square with a 30°–60° set-square against a T-square. Here is the step-by-step reasoning:
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Understanding Set-Squares: Set-squares are drafting tools used to draw precise angles. A 45° set-square typically has angles of 45°, 45°, and 90°, while a 30°–60° set-square has angles of 30°, 60°, and 90°.
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Combining the Set-Squares: By aligning the 45° angle of the 45° set-square with one edge of the T-square and the 30° angle of the 30°–60° set-square with another edge, the interior angle between the non-hypotenuse edges of the set-squares will be 75° (45° + 30° = 75°).
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Using a T-square: The T-square provides a reference straight line against which the set-squares can be aligned accurately, ensuring that the drawn angle is constructed precisely.
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Conclusion: The correct combination as stated would give us the desired angle of 75°, thus making option 4 the correct answer. The use of set-squares against a T-square is a common method in technical drawing to construct various angles precisely without the need for a protractor.
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