Question

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

Step 1

When a radius is drawn to a point of tangency, the angle formed is always a right (90-degree) angle.

Given;

$Arc\text{ RT=24}^o$

Step 2

A)

$\begin{gathered} m\angle WSR=90^{\circ}(Tangent\text{ from a circle\rparen} \\ \end{gathered}$

B)

$m\angle RST=\frac{1}{2}Arc\text{ }RT=\frac{1}{2}(24)=12^{\circ}$

C)

$m\angle WST=90+12=102^{\circ}$