Complete two-column proof:
Given ∠2≅∠4; m∠4=110°
Prove: m∠3=70°
To prove that m∠3 is 70°, we can use the fact that ∠2 is congruent to ∠4. Given that m∠4 is 110°, we can use this information to find m∠3. Here's a step-by-step explanation of a two-column proof:
Statement | Reason
--------------------------------------------------------
1. ∠2 ≅ ∠4 | Given
2. m∠4 = 110° | Given
3. m∠2 = m∠4 | Definition of congruent angles
4. m∠2 = 110° | Substitution using statement 2
5. m∠2 + m∠3 = 180° | Angle sum property of a triangle
6. 110° + m∠3 = 180° | Substitution using statement 4
7. m∠3 = 180° - 110° | Subtraction property of equality
8. m∠3 = 70° | Simplification using statement 7
Thus, we have proved that m∠3 is equal to 70° using the given information and relevant geometry properties.