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;

$\angle ABO+90^{\circ}+68^{\circ}=180^{\circ}$

Adding the values, we have;

$\angle ABO+158^{\circ}=180^{\circ}$

Subtracting both sides by 158, we get;

$\angle ABO=22^{\circ}$

Thus, the measure of ∠ABO is 22°