Question

given ( m angle b w d = m angle e z g )
( m angle 3 = m angle 4 )
prove ( m angle 1 = m angle 2 )

Explanation:

Step1: Use Angle Addition Property

$$m\angle EZG=m\angle 2 + m\angle 4$$

Step2: Substitute using given equalities

Since \(m\angle BWD=m\angle EZG\) (given) and \(m\angle BWD=m\angle 1 + m\angle 3\) (Angle Addition Property), \(m\angle EZG=m\angle 1 + m\angle 3\). Also, \(m\angle 3 = m\angle 4\) (given). Substitute \(m\angle 4\) with \(m\angle 3\) in \(m\angle EZG=m\angle 2 + m\angle 4\), we get \(m\angle EZG=m\angle 2 + m\angle 3\).

Step3: Use Transitive Property

Because \(m\angle EZG=m\angle 1 + m\angle 3\) and \(m\angle EZG=m\angle 2 + m\angle 3\), by transitive property \(m\angle 1 + m\angle 3=m\angle 2 + m\angle 3\).

Step4: Subtract \(m\angle 3\) from both sides

Subtract \(m\angle 3\) from \(m\angle 1 + m\angle 3=m\angle 2 + m\angle 3\). Using subtraction property of equality: \((m\angle 1 + m\angle 3)-m\angle 3=(m\angle 2 + m\angle 3)-m\angle 3\), which simplifies to \(m\angle 1=m\angle 2\).

Answer:

\(m\angle 1 = m\angle 2\)