If all five vertex angles meeting at the center of a regular pentagon are congruent, then each vertex angle of triangle has measure
[tex] \dfrac{360^{\circ}}{5} =72^{\circ}. [/tex]
As known the sum of the measures of three triangle angles is 180° and base angles of isosceles triangle are congruent, then the measure of a base angle of one of the triangles is
[tex] \dfrac{180^{\circ}-72^{\circ}}{2} =\dfrac{108^{\circ}}{2}=54^{\circ} [/tex].
Answer: [tex] 54^{\circ} [/tex].
