Chapter 9.7, Problem 3ST2

To determine

To Find: The $m\stackrel{⌢}{AC}$ shown in figure.

Answer to Problem 3ST2

Measure of arc AC is $82$ .

Explanation of Solution

Given:

  $m\stackrel{⌢}{BD}=80\text{and}\angle 1=80$ .

Figure is shown below.

  

Formula Used:

A theorem state that “the measure of an angle formed by two chords that intersects inside a circle is equal to half the sum of the measure of intercepted arcs.

Calculation:

  $\begin{array}{l}\angle 1=\frac{1}{2}\left(m\stackrel{⌢}{AC}+m\stackrel{⌢}{BD}\right)\\ 81=\frac{1}{2}\left(m\stackrel{⌢}{AC}+80\right)\\ 162=m\stackrel{⌢}{AC}+80\\ m\stackrel{⌢}{AC}=82\end{array}$

Therefore, the answer is $82$ .