Points X and Y are on a circle centered at O, and point Q is outside the circle such that line QX and line QY are tangent to the circle. If angle XQO = 32, then what is the measure of minor arc XY, in degrees?
Arc XY is 142 degrees.
See the following image
Note that OXQY forms a quadrilateral
Since QX and QY are tangent to the circle, then angles QXO and QYO = 90 °
And by symmetry, angle XQY = 2(32) = 64°
And the interior angles of a quadrilateral sum to 360°
QXO + QYO + XQY + XOY = 360
90 + 90 + 64 + XOY = 360
244 + XQY = 360 subtract 244 from both sides
XOY = 116°
And since XOY is a central angle........then minor arc XY has the same measure = 116°