Video Transcript
Find the measure of the reflex
angle 𝐴𝐵𝐶.
In this question, we are asked
to find the measure of the reflex angle 𝐴𝐵𝐶. We can first recall that a
reflex angle is one with measure greater than 180 degrees. So in this case, it is the red
angle at vertex 𝐵. We can also recall that the
measure of an angle is a measure of the amount of rotation required to rotate
one ray onto the other using the vertex as the center of the rotation and that a
full rotation has a measure of 360 degrees. This means if we were to rotate
the ray from 𝐴 through 𝐵 a full turn as shown, then the measure of this angle
is 360 degrees.
We can see that rotating a full
turn is equivalent to rotating through the angle of measure 25 degrees and then
through the red reflex angle. If we call the measure of this
unknown reflex angle 𝑥, then we can say that 25 degrees plus 𝑥 must be equal
to 360 degrees. We can then subtract 25 degrees
from both sides of the equation and evaluate to obtain that 𝑥 is 335
degrees.
We can use the same reasoning
to prove a useful general result. All of the angles around a
point will be equivalent to a full turn. So the sum of the measures of
all of the angles around a point must be 360 degrees.
