What is the measure of angle rps?

Question

Pqr is an equilater triangle. p5 is perpendicular to qr and qs=rs
and that's all I know.
Thanks for your time and patience.
(No one's homework, I assure you.)

Answer 1

I am assuming that p5 is PS

The three angles in an equilateral triangle are equal. Since the sum of the three angles is 180 degree, then each angle must measure 60 degrees.

If QS = RS, then PS is a perpendicular bisector of QR.

It divides the triangle into two congruent right triangles. This also means that PS must bisect angle QPR and the measure for RPS is half the measure of QPR.

The measure for RPS is 30 degrees.

Answer 2

I think you have a few typos in your question. I'm assuming the question is as follows:

PQR is an equilateral triangle. Line ps is perpendicular to side qr and line section qs=rs.

First, it's best if you draw the system out so you can understand the solution. Draw and equilateral triangle and label the verticies of the triangle P, Q, and R. Now draw a line (ps) from angle P to the opposite side (qr) and label the point where the line intersects side qr as "s".

Since PQR is an equilateral triangle, all angles of the triangle are equal and are 60 degrees. Since the original description tells you that qs=rs, the line ps you drew directly bisects both side qr and angle P (ie; splits them exactly in half). So then the angle defined by rps is equal to 60/2= 30 degrees

Answer 3

As I understand if the vertix is at p the angle is 30 degree.
If the verix is at r the angle is 120 degree