Question

2.[–/1 Points]DETAILSALEXGEOM7 6.2.003.MY NOTESASK YOUR TEACHERConsider the following figure. A circle has center point O. There are four points, two interior line segments, and one ray.•Three points lie on the circle:•R is on the left, just below center; •S is on the right, just above center; and •T is on the bottom left.•Point W lies outside the circle, above and slightly left of S.•Segment R S goes from R slightly up and right to S, passing through O.•Segment T S goes from T up and right to S.•Ray S W begins at S and goes up and slightly left through W.Given: circle O with diameter RS, tangent SW , chord TS, and mRT = 24°Find the following in degrees.(a)m∠WSR °(b)m∠RST °(c)m∠WST °

Answer 1

(a)

Since SW is tangent to the circle, the angle formed between the tangent and the diameter is 90°:

m∠WSR = 90°

(b)

Arc RT has a measure of 24°. The inscribed angle is half the measure of the corresponding arc, thus:

m∠RST = 1/2 x 24° = 12°

m∠RST = 12°

(c)

Angle WST is the sum of angle WSR and RST:

m∠WST = m∠WSR + m∠RST

m∠WST = 90° + 12°

m∠WST = 102°