Question

find the measure of the red arc.
the measure of the red arc is \\(\square^\circ\\).

Explanation:

Step1: Set up equation for congruent arcs

When a diameter is perpendicular to a chord, it bisects the chord and its corresponding arcs, so $9x = 80 - x$.

Step2: Solve for $x$

$9x + x = 80$
$10x = 80$
$x = 8$

Step3: Calculate each arc measure

Substitute $x=8$ into $9x$: $9\times8=72$.
Substitute $x=8$ into $80-x$: $80-8=72$.

Step4: Sum arcs for total red arc

Total red arc = $72 + 72$

Answer:

144