An angle formed by a tangent and a chord is measured by _____ its intercepted arc.

When measuring an angle formed by a tangent and a chord, this angle is defined specifically in relation to the arc that it intercepts on the circle. According to the properties of circles in geometry, the relationship is that the angle is measured by one-half of the measure of its intercepted arc.

To understand this concept better, consider how a tangent line intersects a circle at a point and creates both a tangent angle and an intercepted arc. The measure of the angle formed at the point of intersection between the tangent and the chord is determined by taking half of the central angle that subtends the intercepted arc. This means if you were to measure the angle in degrees or radians, it would equate to half of the measure around the circle defined by the intercepted arc.

This principle is foundational in circle geometry and has practical applications in surveying and construction, where accurate angle measurement is crucial for determining locations and layouts.

Choosing the other options would mean misapplying the relationships defined in circle theorems. For instance, measuring the entire arc would not provide the angle's magnitude but would rather give the full extent of the arc between its endpoints without consideration for the constructed angle.