∠ABC and ∠ABD are a linear pair. Prove that m∠ABC + m∠ABD = 180°.
Write a paragraph proof...I don't know how to write this out
Huh? That is the definition of a linear pair -- the two angles form a straight angle.
Not getting the answer
To prove that the sum of the measures of ∠ABC and ∠ABD is equal to 180°, we can use the fact that ∠ABC and ∠ABD form a linear pair. A linear pair consists of two adjacent angles, and the sum of their measures is always 180°. Here is a paragraph proof to demonstrate this:
Given: ∠ABC and ∠ABD form a linear pair.
To Prove: m∠ABC + m∠ABD = 180°.
Proof:
1. By definition, a linear pair consists of two adjacent angles that form a straight line.
2. In this case, ∠ABC and ∠ABD are adjacent angles that share a common vertex and a common side AB.
3. By the definition of a linear pair, the sum of the measures of these two angles is the measure of a straight angle, which is 180°.
4. Therefore, we can conclude that m∠ABC + m∠ABD = 180°.
In this proof, we started by stating the given information and the theorem we want to prove. Then, we used the definition of a linear pair to establish that ∠ABC and ∠ABD satisfy the conditions of a linear pair. Finally, we applied the definition of a straight angle and concluded that the sum of the measures of ∠ABC and ∠ABD is equal to 180°.