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 ?(1 point) Responses 35° 35° 90° 90° 70° 70° 55°
To find the measure of angle B, we need to consider that angle B is an inscribed angle that intercepts the same arc as angle C. The inscribed angle theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.
Since the diameter AB is 14 cm long and AC is 8 cm long, we can find the length of the intercepted arc by subtracting AC from the circumference of the circle:
Circumference = π * diameter
Circumference = π * 14
Circumference ≈ 43.98 cm
Length of intercepted arc = Circumference - AC
Length of intercepted arc ≈ 43.98 - 8
Length of intercepted arc ≈ 35.98 cm
Now, the measure of angle C, which intercepts the same arc as angle B, is half the measure of the intercepted arc:
Angle C ≈ 1/2 * Length of intercepted arc
Angle C ≈ 1/2 * 35.98
Angle C ≈ 17.99
Therefore, the approximate angle measure of B will be 180° - 17.99° = 162.01°. Since this is not among the options given, I believe there may be a mistake in either the information provided or the options.