Answer:
C. 168°
Explanation:
You want the measure of arc YZ intercepted by the angle marked 84° between tangent XY and chord YZ.
Inscribed angle
The measure of an arc intercepted by an inscribed angle is twice the angle measure. Here, that means the measure of the arc is ...
arc YZ = 2 × 84° = 168°
The measure of arc XY is ...
C. 168°
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Additional comment
The angle at the tangent can be considered a limiting case of the inscribed angle ZY'Y where line Y'Y approaches the tangent at Y as Y' approaches Y.
(In this scenario, Y' is on long arc YZ. The inscribed angle ZY'Y will have measure 84° no matter the location of Y' on that arc.)
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