The problem states that angles 1 and 2 are complementary and congruent. Let's break it down:

1. Complementary angles: Two angles are complementary if their measures add up to 90°.
2. Congruent angles: Two angles are congruent if they have the same measure.

Given these conditions, if angles 1 and 2 are congruent, they must have the same measure, and their sum must be 90°. This leads to the following equation:

$\text{Let the measure of angle 1 be } x.$

Since the angles are congruent: $\text{Measure of angle 2 } = x.$

Because the angles are complementary: $x + x = 90^\circ$ $2x = 90^\circ$ $x = \frac{90^\circ}{2} = 45^\circ$

Thus, the measure of angle 1 is 45°.

Would you like more details or have any questions?

Here are five related questions you might find useful:

1. What are the properties of supplementary angles?
2. How do you find the measure of an angle using trigonometry?
3. What are adjacent angles, and how do they differ from complementary angles?
4. How can you prove two angles are congruent?
5. Can angles be complementary if they are obtuse?

Tip: When working with angle relationships, always consider how they interact (complementary, supplementary, etc.) to help solve for unknown angles.