In circle O, and are diameters. Arc ED measures 17°. Circle O is shown. Line segments F C and A E are diameters. Line segments C O and B O are radii. Point B is between points A and C, and point C is between points E and C. Angle D C is a right angle. What is the measure of Arc E F C? 107° 180° 253° 270°
Accepted Solution
A:
Answer:Arc EFC = 253°Step-by-step explanation:Figure attached.We know there are 360 degrees in a circle. Looking at the figure, we can say:Arc EFC + Arc CD + Arc DE = 360Arc CD is 90 degrees since the central angle is 90 degrees given [the central angle of an intercepted arc is equal to the measure of the arc].Arc DE (aka arc ED) is given as 17 degreesNow we plug them into the equation and solve:Arc EFC + Arc CD + Arc DE = 360Arc EFC + 90 + 17 = 360Arc EFC + 107 = 360Arc EFC = 360 - 107Arc EFC = 253Thus, Arc EFC = 253°