Using 30˚ – 60˚ – 90˚ and 45˚ – 45˚ – 90˚ set squares, which of the following angle is not possible to draw?

General
1

using 30˚ – 60˚ – 90˚ and 45˚ – 45˚ – 90˚ set squares, which of the following angle is not possible to draw?

2

LectureNotes said using 30˚ – 60˚ – 90˚ and 45˚ – 45˚ – 90˚ set squares, which of the following angle is not possible to draw?

Answer:

When using 30˚ – 60˚ – 90˚ and 45˚ – 45˚ – 90˚ set squares, you can draw specific angles based on the properties of these triangles. Let’s break down the angles you can achieve with each set square:

30˚ – 60˚ – 90˚ Triangle:

  • 30 degrees: The smallest angle in the triangle.
  • 60 degrees: The middle angle in the triangle.
  • 90 degrees: The right angle in the triangle.

45˚ – 45˚ – 90˚ Triangle:

  • 45 degrees: Both of the non-right angles in the triangle.
  • 90 degrees: The right angle in the triangle.

Possible Combinations:

Using these set squares, you can combine angles to create additional angles:

  • 15 degrees: (45˚ - 30˚)
  • 75 degrees: (45˚ + 30˚)
  • 90 degrees: (45˚ + 45˚ or 60˚ + 30˚)
  • 105 degrees: (60˚ + 45˚)
  • 120 degrees: (60˚ + 60˚)
  • 135 degrees: (90˚ + 45˚)
  • 150 degrees: (90˚ + 60˚)
  • 180 degrees: (90˚ + 90˚)

Angles Not Possible to Draw:

  • 1 degree to 14 degrees (except 15 degrees)
  • 16 degrees to 29 degrees (except 30 degrees)
  • 31 degrees to 44 degrees (except 45 degrees)
  • 46 degrees to 59 degrees (except 60 degrees)
  • 61 degrees to 74 degrees (except 75 degrees)
  • 76 degrees to 89 degrees (except 90 degrees)
  • 91 degrees to 104 degrees (except 105 degrees)
  • 106 degrees to 119 degrees (except 120 degrees)
  • 121 degrees to 134 degrees (except 135 degrees)
  • 136 degrees to 149 degrees (except 150 degrees)
  • 151 degrees to 179 degrees (except 180 degrees)

Conclusion:

Given the angles you can achieve with the 30˚ – 60˚ – 90˚ and 45˚ – 45˚ – 90˚ set squares, any angle not listed above is not possible to draw. For instance, angles like 1 degree, 29 degrees, or 89 degrees are not possible to draw using only these set squares.