Proposition XIII.7 — If three angles of an equilateral pentagon, taken either in …

Proof

The five interior angles sum to

3 \cdot 18 0^{\circ}

(I.32 extended); combined with three equal angles, the constraint forces all five to be equal.

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Depends on (2)

I.32Proposition I.32In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles,…
I.5Proposition I.5In isosceles triangles the angles at the base are equal to one another; and if the equal straight lines be produced…

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