The diameter of circle O is AC¯¯¯¯¯¯¯¯, and mBC⌢=84. What is m∠AOB?
Diameter A C is vertical with A at the top and C at the bottom of the circle. Point B is on the lower right part of the circle.
Responses
48
Pick the answer below.
96
Pick the answer below.
84
Pick the answer below.
174
Pick the answer below.
To solve this problem, we need to use the properties of circles and the relationship between angles and arcs.
Angle AOB is an inscribed angle, and the measure of an inscribed angle is half the measure of its intercepted arc. In this case, arc AC is intercepted by angle AOB.
Since we are given that arc BC has a measure of 84, we know that angle AOB must have a measure of half of that, which is 42 degrees.
Therefore, m∠AOB is 42 degrees.