Q9: The measure of ∠A is half the difference of the intercepted arcs.
.. (55 -12)/2 = 21.5
Q10: Tangents from the same point are congruent.
.. x +15 = 2x -5
.. 20 = x
Q7: The given congruences let you write two equations.
.. -x = y +8
.. -x = 3y +16
Equating the two equations for -x and solving for y gives
.. 3y +16 = y +8
.. 2y = -8
.. y = -4
.. -x = -4 +8 = 4
.. x = -4
Q8: The angle at the intersection is half the sum of the intercepted arcs. (Compare to Q9, where the intersection is external to the circle.)
.. 110 = (97 +x)/2
.. x = 220 -97 = 123
