Question

write a two - column proof of the linear pairs theorem. if ∠abc and ∠cbd are a linear pair, then ∠abc and ∠cbd are supplementary. statements reasons 1) ∠abc and ∠cbd are a linear pair. 1) given 2) m∠abc + m∠cbd = m∠abd 2) angle addition postulate 3) m∠abd = 180 3)

Explanation:

Step1: Recall the given information

We are given that ∠ABC and ∠CBD are a linear - pair.

Step2: Apply the Angle Addition Postulate

By the Angle Addition Postulate, m∠ABC + m∠CBD=m∠ABD.

Step3: Determine the measure of ∠ABD

Since ∠ABC and ∠CBD form a linear pair, ∠ABD is a straight angle. By the definition of straight angles, the measure of a straight angle is 180 degrees. So m∠ABD = 180.

Answer:

1. Definition of straight angles