Given circle A, the measure of arc BD = ...?

[Mathisconfusing101]

Given circle A, the measure of arc BD = ___.

A. 130° B. 140° C. 40°

How would I find the arc?

 

[mcrae]

the acute BD is 140
the obtuse BD is 230

not sure how you know which to use if it wasnt multiple choice, but since it is i'd go with B

 

[Mrspi]

Given circle A, the measure of arc BD = ___.

A. 130° B. 140° C. 40°

How would I find the arc?

First of all, since the arc BD has been named with just TWO letters, we know that it is the minor arc. A major arc is ALWAYS named with THREE letters.

Next, note that arc BD is divided into two parts by point C. The measure of arc BD is the SUM of the measures of the two parts, arcs BC and CD:

m arc BD = m arc BC + m arc CD

The degree measure of an arc is the same as the degree measure of its central angle. The central angle for arc CD has a measure of 90 degrees, so this is also the measure of arc CD. The central angle for arc BC has a measure of 40 degrees, so this is also the measure of arc BC. Substitute:

m arc BD = 40 + 90

Ok?