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How do I draw angles using a ruler and protractor? Specifically, how to draw a 22 degree angle and a 250 degree angle?

Mathematics

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Answers

2 parts
a

an angle of 22∘\text{an angle of } 22^\circ

b

an angle of 250∘\text{an angle of } 250^\circ

Step-by-step solution

11 steps

To draw angles using a ruler and protractor, follow these steps:

Part a· 5 steps

22∘22^\circ

  1. Use a ruler to draw a straight line segment.

    This will be the first arm of your angle. Mark one endpoint of this line as the vertex of the angle.

  2. Place the center of your protractor exactly on the vertex you marked.

    Align the baseline of the protractor with the straight line you drew, ensuring the 0∘0^\circ mark is on the line.

  3. Locate the 22∘22^\circ mark on the protractor scale (usually the inner scale if measuring from the right, or outer scale if measuring from the left).

    Make a small dot on your paper at this mark.

  4. Remove the protractor.

    Use your ruler to draw a straight line segment from the vertex to the dot you made. This is the second arm of your angle.

  5. The angle formed between the two lines is an angle of 22∘\boxed{\text{an angle of } 22^\circ}.

Part b

an angle of 250∘\text{an angle of } 250^\circ

250∘250^\circ

Since a standard protractor measures up to 180∘180^\circ, to draw an angle greater than 180∘180^\circ, you need to use the concept of a reflex angle. A 250∘250^\circ angle is a reflex angle.

  1. Calculate the conjugate angle (the angle that completes a full circle of 360∘360^\circ).

    360∘−250∘=110∘360^\circ - 250^\circ = 110^\circ
  2. Use a ruler to draw a straight line segment.

    Mark one endpoint as the vertex.

  3. Place the center of your protractor on the vertex and align its baseline with the line you drew.

  4. Locate the 110∘110^\circ mark on the protractor scale and make a small dot.

  5. Remove the protractor.

    Use your ruler to draw a straight line segment from the vertex to the dot.

  6. The smaller angle you have drawn is 110∘110^\circ.

    The reflex angle (the larger angle outside the 110∘110^\circ angle, going around the other way) is an angle of 250∘\boxed{\text{an angle of } 250^\circ}.

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