a A regular decagon has 10 sides. Therefore, to create the decagon we need 10 isosceles triangles where the sum of the vertex angles creates 360^(∘).
Therefore, by dividing 360^(∘) by 10 we can determine the measurement of the vertex angle of one such triangle.
360^(∘)/10=36^(∘)
Since these are isosceles triangles, we know by the Base Angles Theorem that the base angles, which we can label θ, are congruent. With this information we can write and solve an equation containing θ.
θ +θ +36^(∘) =180^(∘) ⇔ θ =72^(∘)
b From the exercise we know that we have 10 triangles and that each triangle has an area of 14.5 square inches. Therefore, if we multiply the area of a single triangle by 10, we obtain the area of the regular decagon.
