Question

In the figure above, AB is tangent to the circle with center o at point A.

If AOB has a measure of 68 degrees, what is the measure, in degrees, of ABO?

Answer 1

Given:

Given that O is the center of the circle.

AB is tangent to the circle.

The measure of ∠AOB is 68° and we know that the tangent meets the circle at 90°

We need to determine the measure of ∠ABO.

Measure of ∠ABO:

The measure of ∠ABO can be determined using the triangle sum property.

Applying the property, we have;

`\angle ABO+\angle BAO+\angle AOB=180^(\circ)`

Substituting the values, we get;

`\angle ABO+90^(\circ)+68^(\circ)=180^(\circ)`

Simplifying, we get;

`\angle ABO+158^(\circ)=180^(\circ)`

`\angle ABO=22^(\circ)`

Thus, the measure of ∠ABO is 22°