Video Transcript
In the following figure, find the
measure of angle 𝐷𝑂𝐸.
We begin by recalling that the sum
of the measures of the angles at a point is 360 degrees. And it is also important to note
that we cannot assume that the line from point 𝐶 to point 𝐸 is a straight
line. So we can therefore not use the
properties of supplementary angles. This means that the five angles in
our diagram sum to 360 degrees. We can write this as an equation as
shown. The measure of angle 𝐷𝑂𝐸 plus
the measure of angle 𝐴𝑂𝐸 plus 119 degrees plus 76 degrees plus 41 degrees is
equal to 360 degrees. Summing the three known angles
gives us 236 degrees, and we can therefore simplify our equation. We can then subtract 236 degrees
from both sides such that the measure of angle 𝐷𝑂𝐸 plus the measure of angle
𝐴𝑂𝐸 is equal to 124 degrees.
At this stage, it may not be clear
what to do next. However, let’s consider how the two
unknown angles are labeled on the diagram. This notation tells us that the two
angles are equal. The line 𝑂𝐸 is an angle bisector
such that the measure of angle 𝐷𝑂𝐸 is equal to the measure of angle 𝐴𝑂𝐸. Since the two angles are equal, we
can rewrite our equation as two multiplied by the measure of angle 𝐷𝑂𝐸 is equal
to 124 degrees. And dividing through by two, the
measure of angle 𝐷𝑂𝐸 is equal to 62 degrees. As this also means that angle
𝐴𝑂𝐸 measures 62 degrees, we could add these to our diagram and then check that
all five angles sum to 360 degrees.
