PR and PS are two sides of a square. PS and PT are two sides of a regular pentagon. PR and PT are two sides of a regular polygon with sides. Work out the value of pie .

∠RPT = 18°, ∠PRT = ∠PTR = 81°

Step-by-step 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°

the correct answer would be:

220 centimeters

to get this you can use the pythagorean theorem

hope this

step-by-step explanation: