Question

A regular pentagon is created using the bases of five congruent isosceles triangles, joined at a common vertex.The total number of degrees in the center is 360°. If all five vertex angles meeting at the center are congruent, what is the measure of a base angle of one of the triangles?

Answer 1

It is to be remembered that a a pentagon has five sides. First, we determine each of the central angles by dividing the given sum (360°) by 5. This gives us the answer of 72°. If we let x be the congruent angles in the base and noting that the sum of the internal angles of the triangle is 180°, we have the equation,
                                         72 + x + x = 180°
The value of x from the equation is 54°.