In the diagram below, angle E = 50 degrees, and arc AB, arc BC, and arc CD all have equal length. Find the measure of angle ACD , in degrees.
+128475 3*arc BC + arc AD = 360° ( 1)
(1/2) (arc BC - arc AD) = 50° (2)
angle ACD = (1/2) arc AD (3)
Manipulating (2) we have that
arc BC - arc AD = 100°
arc BC = 100° + arc AD (4)
Sub ( 4) into (1)
3 ( 100 + arc AD) + arc AD = 360°
300 + 4 * arc AD = 360°
4 * arc AD = 360 - 300
4arc AD = 60 °
arc AD = 60 / 4 = 15°
Using (3)
angle ACD = (1/2) (15°) = 7.5°
