angle g is a circumscribed angle of circle e. major arc fd measures 280°. what is the measure of angle gfd…

Answer:

40°

Explanation:

Step1: Find the measure of minor arc FD

The sum of major and minor arcs of a circle is 360°. Given major arc FD = 280°, so minor arc FD = 360° - 280° = 80°.

Step2: Use the property of circum - scribed angle

The measure of a circumscribed angle is half the difference of the measures of the intercepted arcs. Here, the circumscribed angle G intercepts major arc FD and minor arc FD. Also, the measure of an inscribed angle (like ∠GFD) that intercepts an arc is half the measure of the arc it intercepts. The inscribed angle ∠GFD intercepts minor arc FD. So, m∠GFD=$\frac{1}{2}$× minor arc FD. Substituting the value of minor arc FD = 80°, we get m∠GFD = 40°.