A circle has a diameter AB
and an inscribed angle at vertex C
forming triangle ABC
. The measure of angle A
is 27°. Using what you know about inscribed angles, what is the angle measure of B
?
Since angle A is 27°, angle C is the inscribed angle at vertex C and it subtends the same arc as angle A. Therefore, angle C is also 27°.
Since the sum of the angles in a triangle is 180°, we can now find angle B:
angle B = 180° - angle A - angle C
angle B = 180° - 27° - 27°
angle B = 126°.
Therefore, the angle measure of B is 126°.