In regular pentagon ABCDE, diagonal AC is drawn, as shown. Given that each interior angle of a regular pentagon measures 108 degrees, what is the measure of angle CAB?
+23248 Since ABCDE is a regular pentagon, all sides are congruent.
Specifically side(AB) = side(BC).
Therefore,in triangle ABC, angle(BAC) = angle(BCA).
Since the sum of the angles of a triangle is 180°, and angle(ABC) = 108°, leaving 72° for the sum of angle(BAC) and angle(BCA).
Therefore, angle(BAC) is one-half of 72°, or 36°.
