Question

use the given information to prove that m∠abc = m∠edc.
given: m∠1 = m∠4
m∠2 = m∠3
prove: m∠abc = m∠edc

Explanation:

Step1: Express \(m\angle ABC\) and \(m\angle EDC\)

By the angle - addition postulate, \(m\angle ABC=m\angle1 + m\angle2\) and \(m\angle EDC=m\angle3 + m\angle4\).

Step2: Substitute using the given equalities

Since \(m\angle1 = m\angle4\) and \(m\angle2 = m\angle3\), substitute \(m\angle1\) for \(m\angle4\) and \(m\angle2\) for \(m\angle3\) in the expression for \(m\angle EDC\).
We get \(m\angle EDC=m\angle2 + m\angle1\).

Answer:

Since \(m\angle ABC=m\angle1 + m\angle2\) and \(m\angle EDC=m\angle2 + m\angle1\) (by substitution of equal angles), we have \(m\angle ABC = m\angle EDC\) (by the commutative property of addition \(a + b=b + a\)).