Question

in the diagram of circle O, what is the measure of

Answer 1

notice, the external lines to the circle are tangent lines, so, if the small arc by them is 146° as shown there, then the larger arc is 360° - 146°.

check the picture below.

Answer 2

Answer:

The measure of angle ABC is 34°.

Step-by-step explanation:

From the given figure it is clear that the measure of arc AC(minor) is 146 °.

Minor arc + Major arc = 360°

$146+x=360$

$x=360-146=214$

The measure of arc AC(major) is 214 °.

According to the properties of intercepted arc outside the circle, angle ABC is

$\angle ABC=\frac{\text{Major arc AC}-\text{Minor arc AC}}{2}$

$\angle ABC=\frac{214-146}{2}$

$\angle ABC=\frac{68}{2}$

$\angle ABC=34$

Therefore the measure of angle ABC is 34°.