pqr is an equilateral triangle. ps is prependicular to qr and qs=rs. what is the measure of angle rps?

Answer 1

30°
Since all angles of an equilateral triangle measure 60° and the perpendicular line segment ps bisects angle qpr, this means angle rps = 30°.

Good luck!

Answer 2

An equilateral triangle is also equiangular, making each angle 60°ps bisects angle rpq, making rps 60°/2 = 30°.

Answer 3

The answer is 30 degrees for the reasons given above (apart from the person who thinks it can't be answered).

A further check that 30 is the correct answer can be found be looking at the sin of angle rps.

sin rps = rs/rp

rs is half of rq and also half of rp because rq = rp

so sin rps = (1/2(rp))/rp = 1/2

sin rps = 1/2 and as we all know, sin 30 = 1/2

Answer 4

Samantha
I don't think you have given enough information. In mathematics you need two pieces of information to find a third - you have just two. PS is perpendicular to QR, that makes two identical right angle triangles PSR and PQS.
In rational terms the angle RPQ equals two times RPS. Sorry I cant' be of more assistance.

Answer 5

Uhm, both equilateral and equiangular triangles have all their angles measured 60 degree.
so angle rpq is equal to 60 degrees but u put a perpendicular line from point P to line RQ, so P is divided into 2, 60/2=30
so its 30 degrees
Thats it!

Answer 6

And to boot, Napoleon thought the question could not be answered EVEN AFTER THREE PEOPLE HAD ALREADY ANSWERED IT, and given very good explanations for their answers.