
Angles 1 and 2 are complementary and congruent. What is the measure of angle 1?

30°  

45°

50°

75°

Since angles 1 and 2 are complementary, their measures add up to 90°. They are also congruent, meaning they have the same measure. Let's call the measure of angle 1 "x." 

Because the angles are congruent, the measure of angle 2 is also "x." Therefore:

\[
x + x = 90°
\]

Simplifying:

\[
2x = 90°
\]

Now, solve for \(x\):

\[
x = \frac{90°}{2} = 45°
\]

So, the measure of angle 1 is **45°**.

Would you like more details or have any questions?

Here are five related questions:
1. What is the definition of complementary angles?
2. How do congruent angles differ from supplementary angles?
3. Can two obtuse angles be complementary?
4. What is the measure of each angle if they are supplementary and congruent?
5. How do you determine the complement of an angle?

**Tip:** When two angles are complementary, their sum will always equal 90°, regardless of their individual measures.

Angles 1 and 2 are complementary and congruent. What is the measure of angle 1?

Explore how to find the measure of angle 1 when two angles are both complementary and congruent. This geometry problem highlights the properties of complementary and congruent angles and uses simple equations to find the solution. Ideal for students in Grades 6-8.

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