Question

Write a complete two-column proof for the following information. Hint: Use the Angle Addition Theorem and the fact that a line is made up of two opposite rays.

Given: m∠1 = 62° and lines t and l intersect
Prove: m∠4 = 62°
A) Statement 1: m∠1 = 62°, Statement 2: Given, Reason 1: Given
B) Statement 1: m∠1 + m∠4 = 180°, Statement 2: Linear pair theorem, Reason 1: Definition of a linear pair
C) Statement 1: m∠1 = 62°, Statement 2: Given, Reason 1: Given
D) Statement 1: m∠1 = 62°, Statement 2: Linear pair theorem, Reason 1: Definition of a linear pair

Answer 1

To prove m∠4 = 62°, you can use the Angle Addition Theorem and the fact that a line is made up of two opposite rays. Here is a complete two-column proof using these concepts.

Step-by-step explanation:

To prove that m∠4 = 62°, you can use the Angle Addition Theorem and the fact that a line is made up of two opposite rays.

Here is a complete two-column proof:

Statement 1: m∠1 = 62°

Statement 2: Given

Reason 1: Given

Statement 3: m∠1 + m∠4 = 180°

Statement 4: Angle Addition Theorem

Reason 2: Definition of a linear pair

Statement 5: 62° + m∠4 = 180°

Statement 6: Substitution

Statement 7: m∠4 = 62°

Statement 8: Subtraction property of equality

Reason 3: Algebraic property

Therefore, it is proven that m∠4 = 62°.