Question

explore the angles of a circle by following these steps.

1. move point g to point a and move point l to point b and observe how the angle measures change.
2. the measure of the circumscribed ∠ghl is 59° when the points of tangency are a and b.
3. the sum of the measures of the central angle and the circumscribed angle is

m∠acb = 121°
m∠ghl = 59°

Explanation:

Step1: Identify the given angles

We know that \( m\angle ACB = 121^\circ \) (central angle) and \( m\angle GHL=59^\circ \) (circumscribed angle).

Step2: Calculate the sum of the angles

To find the sum, we add the measures of the central angle and the circumscribed angle. So, we calculate \( 121^\circ + 59^\circ \).

\[
121^\circ+ 59^\circ=180^\circ
\]

Answer:

\( 180^\circ \)