Ask AI on The Internet
Question: If it is given that L is parallel to N, then prove that the measure of angle 2 and the measure of angle 7 add up to 180 degrees by creating a two column proof but you can only use angles 6, 7, and 2 and it gives you the statements, but you have to come up with the reasons. The statements are: L is parallel to N, angles 7 and 6 are supplementary, the measure of angles 7 and 6 add up to 180, angle 6 is congruent to angle 2, the measure of angle 6 is equal to the measure of angle 2, the measure of angles 7 and 2 add up to 180
Two-column Proof: | Statements | Reasons | |--------------------------------------------|-------------------------------------| | 1. L is parallel to N | Given | | 2. Angles 7 and 6 are supplementary | Given | | 3. The measure of angles 7 and 6 add up to 180 | Definition of Supplementary Angles | | 4. Angle 6 is congruent to Angle 2 | Corresponding Angles Postulate | | 5. The measure of Angle 6 is equal to the measure of Angle 2 | Definition of Congruent Angles | | 6. The measure of angles 7 and 2 add up to 180 | Substitution Property of Equality | Let me explain: Step 1: The first statement mentions that Lines L and N are parallel, which is provided in the problem. Step 2: The problem also states that angles 7 and 6 are supplementary, which means their measures add up to 180 degrees. Step 3: From the definition of supplementary angles, we can conclude that the measure of angles 7 and 6 add up to 180 degrees. Step 4: If lines are parallel, corresponding angles are congruent. Therefore, Angle 6 is congruent to Angle 2, since they are corresponding angles in parallel lines. Step 5: Two angles are congruent if they have the same measure, so the measure of Angle 6 is equal to the measure of Angle 2. Step 6: Finally, we can replace the measure of Angle 6 with the measure of Angle 2 in the 1st equation (from step 3) to get "the measure of angles 7 and 2 add up to 180", by the substitution property of equality. This completes the proof.
A new large language model has been made available since this question was asked.
To generate an updated answer from the new model, click the button below.
Think your answer is better than the AI's? Post it below.
Question Tags
If you want your question answered by an AI, click here.
Post your own comment: