Answer:
B) The measure of arc CR is 92°.
Explanation:
An arc measure is equal to its corresponding central angle measure.
Therefore, if a straight line is drawn from point C on the circumference to the center of the circle, the measure of angle COR is equal to the measure of arc CR.
Line segment CO is equal to line segment OR, as both these segments are the radius of circle O. Therefore, triangle COR is an isosceles triangle. The base angles of an isosceles triangle are equal, so as m∠CRO = 44° then m∠RCO = 44°.
Interior angles of a triangle sum to 180°. Therefore:
⇒ m∠COR + m∠CRO + m∠RCO = 180°
⇒ m∠COR + 44° + 44° = 180°
⇒ m∠COR + 88° = 180°
⇒ m∠COR + 88° - 88° = 180° - 88°
⇒ m∠COR = 92°
Since the measure of arc CR is equal to the central angle COR, the measure of arc CR is 92°.