Before we take a look at the given diagram, let's start by defining complementary angles.
Complementary Angles
Two positive angles whose measures have a sum of 90^(∘).
Now, let's consider the given diagram.
Since ∠ EAD is a right angle, its measure is 90^(∘). As points E, A, and B all lie on the same line, m∠ EAB = 180^(∘).
As angles ∠ EAD and ∠ BAD share a side AD, they are adjacent angles. The sum of their measures equals 180^(∘), the measure of ∠ EAB. Therefore, the measure of ∠ BAD is 180^(∘) - 90^(∘) = 90^(∘).
Now, notice that ∠ DAC and ∠ CAB are a pair of adjacent angles, so the sum of their measures equals the measure of ∠ BAD — 90^(∘). As a result, ∠ DAC and ∠ CAB are a pair of complementary angles.
