In circle E, angle G is defined as a circumscribed angle that intercepts the major arc FD, which measures 280 degrees. This situation presents an interesting geometrical concept where the position of angle G relative to the circle and the arc significantly influences its measurement.
A circumscribed angle is one that is formed outside the circle by two lines that extend from points on the circle. In this case, angle G is created by the lines connecting points F and D, which lie on the circumference of circle E. When we talk about the measure of the arc, it’s important to note that a full circle measures 360 degrees. Therefore, the remaining minor arc, which does not include the points F and D but rather the shorter path around the circle, measures:
360 degrees – 280 degrees = 80 degrees
According to the properties of circumscribed angles, the measure of angle G is half the difference of the measures of the intercepted arcs. Since angle G intercepts major arc FD, the relationship can be expressed as:
Measure of angle G = 1/2 (measure of arc FD – measure of minor arc)
Plugging in our values, we calculate:
Measure of angle G = 1/2 (280 degrees – 80 degrees) = 1/2 (200 degrees) = 100 degrees
Thus, the measure of angle G is 100 degrees, showcasing how a circumscribed angle relates intricately to both the major arc intercepted and the geometric properties of the circle itself. This relationship is fundamental in understanding how angles and arcs function together within circle geometry.