Question

Please help me with this

Answer 1

For part A, if P is the center of that triangle, then PR and PT have the same length; therefore, triangle RPT is isosceles.  For part B, by the definition of an incenter...if P is an incenter, then it is the place where all the angle bisectors meet.  Therefore, angles SRP and PRT are congruent, as are angles STP and PTR.  Since the vertex angle measures 64, then each of the base angles by the isosceles triangle theorem measure 58.  Half of 58 makes the base angles within the smaller triangle measure 29.  And if both of those measure 29, by the triangle angle-sum theorem, 180-29-29 = 122  And that's the measure of angle RPT.  Eek.