Find the sum of the two adjacent
angles from the given angles in the diagram.
We begin by recalling the
definition of adjacent angles. Two angles are adjacent if they
have the same vertex, have a common side, and their distinct sides lie on opposite
sides of the common side. We can see from the diagram that we
have three angles that measure 22, 64, and 88 degrees. All three angles share a common
vertex. However, it is only the angles of
measures 64 degrees and 88 degrees that share a common side. The distinct sides of these two
angles do lie on opposite sides of the common side. We can therefore conclude that 64
degrees and 88 degrees are the adjacent angles. We are asked to find the sum of
these. Since 64 plus 88 is 152, the sum of
the two adjacent angles in the diagram is 152 degrees.
It is worth noting that adding the
measures of the two adjacent angles is equivalent to finding the measure of the
combined angle, that is, the angle between the distinct sides of the adjacent