Question

in circle o, \\(\overline{ac}\\) and \\(\overline{bd}\\) are diameters. what is \\(m\widehat{bc}\\)? \\((3x - 70)\degree\\) \\((x + 10)\degree\\) \\(\bigcirc\\ 50\degree\\) \\(\bigcirc\\ 80\degree\\) \\(\bigcirc\\ 100\degree\\) \\(\bigcirc\\ 130\degree\\)

Explanation:

Step1: Identify vertical angles

$\angle AOB = \angle COD$, so $3x - 70 = x + 10$

Step2: Solve for x

$3x - x = 10 + 70$
$2x = 80$
$x = 40$

Step3: Find $\angle AOB$

Substitute $x=40$: $3(40) - 70 = 120 - 70 = 50^\circ$

Step4: Calculate $m\overset{\frown}{BC}$

$\angle AOB + \angle BOC = 180^\circ$, so $m\overset{\frown}{BC} = 180^\circ - 50^\circ = 130^\circ$

Answer:

130°