Question

If angle SUT is 39, what does that tell us about angle TUV? What arc measure describes arc VTS? How can we make any assertions about these angle and arc measures? b. Which line segments’ length can be calculated based on knowing the radius length? Explain. c. If angle MOP is 49, which other angle measures can we calculate? What arc measures can we calculate? Describe which lesson concepts allow us to make these calculations.

Answer 1

Part a:
The diameter of a circle bisects two intersecting tangents.
In the given diagram, OU is the diameter of the circle and SU and VU are tangents to the circle.
Angle SUT = TUV. Since angle SUT is 39, angle TUV = 39.

The arc measure that describes arc VTS is mVS

Part b
Knowledge of the radius length helps in the calculation of the line segments MT, MO, OT and NS.

Part c
If angle MOP = 49, then angle QTR can be calculated as 90 - 49 = 41. Also, angle MQR is calculated as 180 - 49 = 131