Angle xyz is an inscribed angle (its vertex is on the circle). Angle xcz is a central angle (its vertex is at the circles center). When two such angles intercept (or cut off) the same arc of the circle, a specific size relationship exists between the two angles. The measure of the central angle will always be double the measure of the inscribed angle. In this case, that means that the measure of angle xcz must be 80. Thus, minor arc xz also measures 80. Every circle (considered as an arc) measures 360. This means major arc xyz measures 280 (360 80).
Answer Anonymously
Copy Link
