line segment bd is a diameter of circle e. what is the measure of arc bc? 39° 78° 102° 129°
line segment bd is a diameter of circle e. what is the measure of arc bc? 39° 78° 102° 129°
Answer
Explanation:
Step1: Recall the inscribed - angle theorem
The measure of an inscribed angle is half the measure of the intercepted arc. In the circle with center (E), (\angle BDC = 51^{\circ}) is an inscribed angle and it intercepts arc (BC).
Step2: Calculate the measure of arc (BC)
Let the measure of arc (BC) be (x). According to the inscribed - angle theorem, (m\angle BDC=\frac{1}{2}m\overset{\frown}{BC}). So, (x = 2\times m\angle BDC). Substitute (m\angle BDC = 51^{\circ}) into the formula: (x=2\times51^{\circ}=102^{\circ}).
Answer:
(102^{\circ})