Question

which angle cannot be constructed with ruler and compass

Answer 1

123° 

239°

etc etc . such angles cannot be constructed with ruler and compass

Answer 2

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Which angle cannot be constructed with ruler and Compass ?

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• 5°

• 10°

• 20°

• 40°

• 50°

• 70°

• 80°

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Suppose that we have same Question that Which of the following angle cannot be constructed with ruler and Compass ?

• 150°

• 120°

• 60°

• 40°

Correct - 40°

Explanation

30°,45°,60°,90° are considered special angles.

40° can be expressed as the sum of the following angles.

40° = 30° + 10° or 40° = 20° + 20°

We can note that 30° is a special angle but 20° and 10° are not.

Hence,40° cannot be written as a combination of special angles and is not possible to construct using a ruler and a compass.