Question

If arc mAC = 106 what is angle mABC? 

53°
74°
86°
128°

Answer 1

hmm is the same "far arc - near arc" formula.

recall that a circle has a total of 360°, so if the minor arc of AC is 106°, the major arc of AXC has to be 360 - 106 or 254°.


`\bf \stackrel{\textit{far arc - near arc formula}}{\measuredangle ABC=\cfrac{254-106}{2}}\implies \measuredangle ABC = \cfrac{148}{2}\implies \measuredangle ABC=74`