Find the measure of angle BAC.
{There's an image of a circle with an angle from the top
left side going to the bottom of the right side. Point A
is the point at the top left side starting the angle, and
B is at the bottom and point C is at the bottom right side.
Inside the angle is a central angle BOC which measures 57degrees. point O is at the side of the larger angle, points
B and C are at the bottom.}
33degrees
57degrees
114degrees
28.5degrees
To find the measure of angle BAC, we need to use the information given in the diagram.
From the diagram, we can see that angle BOC is a central angle inside the larger angle BAC, and it measures 57 degrees.
In a circle, a central angle is an angle whose vertex is at the center of the circle, and its arms intersect the circumference of the circle.
Since angle BOC is a central angle, its measure is equal to the measure of the arc it intercepts on the circumference of the circle.
Given that angle BOC measures 57 degrees, we can conclude that the arc it intercepts on the circumference of the circle also measures 57 degrees.
Now, we can use the fact that the sum of the measures of an inscribed angle and its intercepted arc is always 180 degrees.
Angle BOC is an inscribed angle with its intercepted arc measuring 57 degrees. Therefore, the measure of the inscribed angle BAC is the same as the measure of the intercepted arc.
Hence, angle BAC measures 57 degrees.