Complete the two column proof. given 2=4 m<2=110 prove m<3=70
Statements Reasons
1. 2 = 4 Given
2. m∠2 = 110 Given
3. ∠2 and ∠3 are supplementary Definition of supplementary angles
4. m∠2 + m∠3 = 180 Sum of angles in a straight line is 180 degrees
5. m∠3 + m∠2 = 180 Commutative property of addition
6. m∠3 + 110 = 180 Substitution (from statement 2)
7. m∠3 = 180 - 110 Subtraction property of equality
8. m∠3 = 70 Simplification
To complete the proof, we need to show the logical steps based on the given information and the properties of angles. Here is the completed two-column proof:
Statement | Reason
-------------------------------------
1. 2 = 4 | Given
2. m < 2 = 110 | Given
3. m < 2 + m < 3 = 180 | Angle sum theorem
4. 110 + m < 3 = 180 | Substitution property using statement 2
5. m < 3 = 70 | Subtracting 110 from both sides using statement 4
Therefore, we have proven that m < 3 = 70 based on the given information.
To complete the two-column proof, we need to provide a sequence of logical statements and reasons to show that m<3 is equal to 70 given that 2=4 and m<2=110.
Here is a step-by-step explanation of the proof:
Statement: 2 = 4 Given
Reason: Given information
Statement: m<2 = 110 Given
Reason: Given information
Statement: m<2 + m<3 = 110 + m<3 Adding m<3 to both sides of the equation
Reason: Addition property of equality
Statement: 4 + m<3 = 110 + m<3 Replacing 2 with 4 (using the given information)
Reason: Substitution property
Statement: 4 = 110 Subtracting m<3 from both sides of the equation
Reason: Subtraction property of equality
Statement: m<3 + 4 = m<3 + 110 Adding m<3 to both sides of the equation
Reason: Addition property of equality
Statement: 4 = 110 Subtracting m<3 from both sides of the equation
Reason: Subtraction property of equality
Statement: m<3 = 70 Combining like terms
Reason: Subtraction property of equality
Therefore, we have proven that m<3 = 70, using the given information that 2=4 and m<2=110, and a sequence of logical statements based on the properties of equality.