Question

Find the value of z.

Answer 1

The exterior angle at the intersection of the tangent and secant has a measure that is half the difference between the intercepted arcs.

... ((10x+20) -80)/2 = 2x+15

... 5x -30 = 2x +15

... 3x = 45

... x = 15

So, the unknown arc to the right has measure

.. 10x + 20 = 10·15 +20 = 170

And the arcs of the circle total 360°.

... 80 + z + 170 = 360

... z = 360 - 250 = 110 . . . subtract 250 from both sides

The appropriate choice for the value of z is

... B. 110