Regina draws a triangle inside a circle; she labels the vertices ABC , with the diameter as AB and the inscribed angle as C . She draws the length of AB 14 cm long, and AC 8 cm long. Using what you know about inscribed angles, what will be the approximate angle measure of B ?
Since triangle ABC is inscribed in a circle, angle C is an inscribed angle that intercepts the same arc as AB. By the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of the intercepted arc.
Since the diameter AB intercepts the entire circle, the arc intercepted by angle C is the full circumference of the circle. The circumference of a circle with a diameter of 14 cm is π*14 = 44 cm.
Therefore, the measure of angle C is half the measure of the circumference of the circle, which is 44/2 = 22 cm.
Since angle B is the supplementary angle to angle C, the measure of angle B is 180 - 22 = 158 degrees.
Therefore, the approximate angle measure of B would be 158 degrees.