To determine the measure of angle 1, we need to understand the properties of complementary and congruent angles. Complementary angles are two angles whose measures add up to 90 degrees. Congruent angles have equal measures.
Given that angle 1 and angle 2 are complementary, we can express this relationship mathematically:
Measure of Angle 1 + Measure of Angle 2 = 90 degrees
Since angle 1 is congruent to angle 2, we can also state that:
Measure of Angle 1 = Measure of Angle 2
Now, let’s denote the measure of angle 1 as ‘x’. Therefore, we can rewrite the relationship:
x + x = 90 degrees
This simplifies to:
2x = 90 degrees
Dividing both sides by 2 gives us:
x = 45 degrees
Thus, the measure of angle 1 is 45 degrees. Since angle 1 and angle 2 are congruent, angle 2 also measures 45 degrees.