Dodecagon

Calculate the size of the smaller angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.

Correct answer:

x =  75 °

Step-by-step explanation:

n=12 φ=n360​=12360​=30 ∘ A1​=1⋅ φ=1⋅ 30=30 ∘ A2​=2⋅ φ=2⋅ 30=60 ∘ A4​=4⋅ φ=4⋅ 30=120 ∘ A10​=10⋅ φ=10⋅ 30=300 ∘  s1​=2A4​−A1​​=2120−30​=45 ∘ s2​=2A10​−A2​​=2300−60​=120 ∘  x1​=s2​−s1​=120−45=75 ∘ x2​=180−x1​=180−75=105 ∘  x=x1​=75=75∘

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