The base angles of the isosceles triangles are supplementary to the angles of the regular pentagon. To calculate the angles of the regular pentagon use the formula (n-2)180^(∘)n, where n is the number of sides in the pentagon.
A regular pentagon has five congruent angles. Therefore, we can calculate the measure of each angle by using the following formula.
(n-2)180^(∘)/n
In this formula n is the number of vertices in the polygon.
Each of the pentagon's angles is 108^(∘). Let's add that to the diagram.
Notice that the isosceles triangle's base angles are all supplementary to one of the pentagon's angles. With this information we can calculate the triangle's base angles.
180^(∘)-108^(∘)=72^(∘)
The isosceles triangle has base angles of 72^(∘). Using the Interior Angles Theorem, we can determine the vertex angle.
72^(∘)+72^(∘)+m∠ θ = 180^(∘)
⇓
m∠ θ = 36^(∘)
