Line segment BD is a diameter of circle E.

Circle E is inscribed with triangle B C D. LIne segment B D is a diameter. Line segments D C and C B are secants. Angle D B C is 51 degrees.
What is the measure of arc B C?

39°
78°
102°
129°

78 degrees

Step-by-step explanation:

Mainly because the measure of the arcs intercepted by the interior angles equals 2 times those interior angles.

so arc DC =  2 * angle DBC = 2 * 51 degrees = 102 degrees.

We also see that because BD is a diameter the angle  BCD that intercepts it is 90 degrees because   half-circle arc BD = 2 * angle BCD

180 degrees = 2 * angle BCD

also we want arc BC.

we know that the total circle is the sum of all 3 arcs.

arc BC + (half-circle) arc BD + arc DC = 360 degrees

arc BC + 180  + 102 = 360 degrees.

arc BC =  360 - 180 - 102 = 78 degrees

175

step-by-step explanation:

2 inches x 10 miles = 200 miles - 3 inches = 175