Answer:
∠RPT = 18°, ∠PRT = ∠PTR = 81°
Explanation:
First we would find the draw the diagram obtained from the given information. Then we would work out the angles of RPT, PRT and PTR.
Given:
PR and PS are two sides of a square
PR = PS (all the sides of a square are equal)
PS and PT are two sides of a regular pentagon
PS = PT (all sides of a pentagon are equal)
PR and PT are two sides of both polygons
Sum of interior angles = 180(n-2)
Pentagon has 5 sides, n = 5
180(5-2) = 540°
Each interior angles = 540/5 = 108°
∠SPT = ∠SPR + ∠RPT
∠SPT = 108°, ∠SPR = 90°
108 = 90+ ∠RPT
∠RPT = 108-90 = 18°
PT = PR (the side of the square has the same length as the side of
the regular pentagon)
This makes ∆RPT an isosceles
Let = ∠PRT = ∠PTR =x
2x + ∠RPT = 180° (sum of angles in a triangle)
2x = 180-18 = 162
x = 162/2 = 81°
∠PRT = 81°
∠PTR = 81°