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Seeking The Angle (Posted on 2007-10-29) Difficulty: 2 of 5
A point S is taken on the side QR of triangle PQR such that RS = 2SQ. It is known that Angle PQR = 45o and Angle SPQ = 15o

Determine Angle PRQ.

See The Solution Submitted by K Sengupta    
Rating: 2.0000 (1 votes)

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Solution Geometer's Sketchpad answer | Comment 1 of 4

Start with a line. Erect a perpendicular. Using a point on each line, bisect the angle, making the 45-degree angle at Q.

Using arbitrary point C on the perpendicular as a center and twice its distance to Q as a radius, construct a circle, intersecting the original line at P. Bisect CPQ. The bisector cuts the bisector of the 90-degree angle at S. Measure off twice QS from S to R.

Geometer's Sketchpad now shows angle PRQ to be 75 degrees.

  Posted by Charlie on 2007-10-29 11:47:30
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