Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s). points a and b are the endpoints of an arc of a circle. chords are drawn from the two endpoints to a third point, c, on the circle. given m\\(\overarc{ab}\\) = 64° and \\(\angle abc\\) = 78°, m\\(\angle acb\\) = \\(\square\\) ° and m \\(\overarc{ac}\\) = \\(\square\\) °.

Explanation:

Step1: Find $m\angle ACB$

An inscribed angle is half its arc.
$m\angle ACB = \frac{1}{2}m\overset{\frown}{AB} = \frac{1}{2} \times 64^\circ = 32^\circ$

Step2: Find $m\overset{\frown}{AC}$

An inscribed angle is half its arc.
$m\overset{\frown}{AC} = 2 \times m\angle ABC = 2 \times 73^\circ = 146^\circ$

Answer:

$m\angle ACB = 32$ and $m\overset{\frown}{AC} = 146$