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
\(Angle (1)=\frac{1}{2}*(80\°-40\°)=20\°\)
therefore
the answer Part a) is
∠1 =\(20\°\)
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
\(Angle (2)=\frac{1}{2}*(70\°+30\°)=50\°\)
the answer Part b) is
∠2 =\(50\°\)
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
\(Angle (3)=\frac{1}{2}*(60\°-30\°)=15\°\)
therefore
the answer Part c) is
∠3 =\(15\°\)
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
\(PT*PU=PS*PV\)
we have
\(PS=12\ units\\PV=PS+VS=12+9=21\ units\\PU=PT+UT=PT+4\)
substitute
\(PT*(PT+4)=12*21\)
\(PT^{2} +4PT-252=0\)
using a graphing tool------> to resolve the second order equation
see the attached figure
the solution is
\(PT=14\ units\)
therefore
the answer Part d) is
\(PT=14\ units\)
