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The problem asks to prove that the measure of angle 3 is 113°, given that angles 1 and 2 are complementary, with \( m \angle 1 = 23^\circ \).

### Two-Column Proof:

| Statement                                      | Reason                           |
|------------------------------------------------|----------------------------------|
| 1. \( m \angle 1 = 23^\circ \)                 | Given                            |
| 2. \( \angle 1 \) and \( \angle 2 \) are complementary | Given                            |
| 3. \( m \angle 1 + m \angle 2 = 90^\circ \)    | Definition of complementary angles|
| 4. \( m \angle 2 = 90^\circ - 23^\circ = 67^\circ \) | Subtraction property of equality |
| 5. \( \angle 2 \) and \( \angle 3 \) form a linear pair | Given (based on the diagram)     |
| 6. \( m \angle 2 + m \angle 3 = 180^\circ \)   | Linear pair postulate            |
| 7. \( m \angle 3 = 180^\circ - 67^\circ = 113^\circ \) | Subtraction property of equality |

Thus, \( m \angle 3 = 113^\circ \) is proven.

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Would you like a more detailed explanation of any step? Here are 5 related questions for deeper understanding:

1. What are complementary angles?
2. How do we know angles form a linear pair?
3. What other types of angle relationships exist in geometry?
4. Can complementary angles also be adjacent?
5. How can we apply the linear pair postulate in different scenarios?

**Tip**: Remember that complementary angles always sum up to \( 90^\circ \), while a linear pair of angles sums to \( 180^\circ \).

Given: ∠1 and ∠2 are complementary. m∠1 = 23°. Prove: m∠3 = 113°.

This problem asks to prove that the measure of angle 3 is 113°, given that angles 1 and 2 are complementary and m∠1 = 23°. Explore key concepts like complementary angles, the linear pair postulate, and step-by-step proofs. Suitable for Grades 8-10.

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