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

The measure of angle ABC is 34°.

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=(214-146)/(2)`

`\angle ABC=(68)/(2)`

`\angle ABC=34`

Therefore the measure of angle ABC is 34°.