Answer:
122°
Explanation:
The sum of the measures of the angles of a triangle is 180°. Since m∠RST = 64°, this means that the other two angles must equal
180-64 = 116°.
We know from the diagram that RST is an isosceles triangle. This means that the base angles, ∠SRT and ∠STR, are congruent; this means each of them would equal
116/2 = 58°.
RP will bisect ∠RST, and PT will bisect ∠STR. This means that ∠PTR = 58/2 = 29° and ∠PRT = 58/2 = 29°.
This means the base angles are 29+29 = 58°; this leaves 180-58 = 122° for ∠RPT.