Given that the measure of angle
𝐴𝑂𝐵 is 75 degrees, what is the measure of angle 𝐵𝑂𝐶?
In this question, we are given a
figure and the measure of an angle in that figure. We need to use this to determine
the measure of the other angle in the figure.
To answer this question, we can
start by adding the two angles and the given measure onto the given diagram. We are told that the measure of
angle 𝐴𝑂𝐵 is 75 degrees. We want to find the measure of
angle 𝐵𝑂𝐶. Remember, the second point in the
angle is the vertex of the angle. This can help us mark the angles on
We can now note that these two
angles are adjacent, since they share a vertex at 𝑂 and they have the ray from 𝑂
through 𝐵 as a common side and the angles do not overlap. We can then recall that the sum of
the measures of adjacent angles is equal to the measure of the angle between their
distinct sides. We can see in the diagram that this
is a right angle, so its measure is 90 degrees. Since a right angle has a measure
of 90 degrees, this means that the angles are complementary angles. And the sum of their measures is 90
We can now solve this equation for
the measure of angle 𝐵𝑂𝐶 by substituting in the measure of angle 𝐴𝑂𝐵 is 75
degrees. We then subtract 75 degrees from
both sides of the equation to get that the measure of angle 𝐵𝑂𝐶 is equal to 90
degrees minus 75 degrees, which we can calculate is equal to 15 degrees.