Part a) If m VU= 80° and m ST= 40°, then ∠1 =
we know that
The measurement of the external angle is the semi-difference of the arcs it comprises.
so
therefore
the answer Part a) is
∠1 =
Part b) If m VU= 70° and m ST= 30°, then ∠2 =
we know that
The measure of the internal angle is the semi- sum of the arcs comprising it and its opposite.
so
the answer Part b) is
∠2 =
Part c) If m VB= 60° and m BS = 30°, then ∠3 =
we know that
The measurement of the external angle is the semi-difference of the arcs it comprises.
so
therefore
the answer Part c) is
∠3 =
Part d) If VS = 9, SP = 12 and UT = 4, then TP =
we know that
The Intersecting Secants Theorem states that when two secant lines intersect each other outside a circle, the products of their segments are equal.
so
we have
substitute
using a graphing tool------> to resolve the second order equation
see the attached figure
the solution is
therefore
the answer Part d) is