A tangent line and a chord meet at the point of tangency, forming a tangent-chord angle of 40°. What is the measure of the intercepted arc?

The angle formed by a tangent and a chord at the point of tangency equals half the measure of the arc it intercepts. So the arc is twice the angle: $2\cdot40^\circ=80^\circ$, choice H. This is similar to the inscribed angle rule, in which an angle that has its vertex on the circle is half its arc. Choice G ($40^\circ$) reports the angle itself instead of the arc. Choice F ($20^\circ$) halves the angle, going the wrong way. Choice J ($160^\circ$) doubles twice. The intercepted arc is always larger than the tangent-chord angle.