Seeking The Angle (Posted on 2007-10-29)

	Submitted by K Sengupta
Rating: 3.5000 (2 votes)
Solution:	(Hide)
Angle PRQ = 75 degrees. EXPLANATION: We draw RX perpendicular to SP, so that X lies on SP. We now join XQ. Then Angle PSR = Angle PQS + Angle SPQ = 60 degrees. Now, in triangle RXS, Angle XRS = 90 degrees – Angle XSR = (90 – 60) degrees = 30 degrees. So, XS/SR = sin 30 = 1/2 Or, RS = 2XS……..(i) Now, RS = 2SQ gives XS = QS, Thus, Angle XSQ = Angle SQX = = (1/2)*Angle RSX = 60/2 = 30 degrees Hence, Angle PQX = 45 – Angle XQS = 45 – 30 = 15 degrees. Accordingly Angle PQX = Angle XPQ = 15 degrees, so that triangle PQX is isosceles with PX = XQ. But, since Angle XRQ = Angle XQR, it follows that XR = XQ, and accordingly, we must have PX=XR Therefore, Triangle RXP is isosceles right angled triangle, so that: Angle XRP = Angle XPR = 45 degrees. Consequently: Angle PRQ = Angle PRX + Angle XRS = 45 + 30 = 75 degrees. ----------------------------------------------- Also, refer to the solution submitted by Bractals in this location.

	Subject	Author	Date
	re: Solution	K Sengupta	2008-03-10 14:49:21
	Solution	Dej Mar	2007-10-30 00:06:39
	Solution	Bractals	2007-10-29 12:04:57
	Geometer's Sketchpad answer	Charlie	2007-10-29 11:47:30