We will find the measures of ∠RCY,∠RCZ, and ∠ZRC one at a time.
Finding m∠RCY
The radii divide the regular octagon into eight congruent isosceles triangles. Since corresponding angles of congruent figures are congruent, the vertex angles of the isosceles triangles formed by the radii are congruent. Moreover, since a full turn measures 360∘, we can divide 360∘ by 8 to obtain their measures.
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