Given: circle O with diameter RS, tangent SW, chord TS, and mRT = 34°.Find the following in degrees. (a) m∠WSR (b) m∠RST (c) m∠WST

Question

Consider the following figure.

	Given:  circle O with diameter RS, tangent SW, chord TS, and mRT = 34°

Find the following in degrees.

(a) m∠WSR

 

(b) m∠RST

 

(c) m∠WST

Answer 1

a) If a tangent line and radius (or diameter) meet at the point of tangency, then they are perpendicular. Hence m∠WSR = ___?

b) Angle RST intercepts arc RT, which is 34°. The measure of an inscribed angle is 1/2 the measure of its intercepted arc. Hence m∠RST = _____?

c) m∠WST = m∠WSR + m∠RST = _____? You know m∠WSR and m∠RST from (a) and (b).