Question

statements reasons 1. ( mangle cad=mangle ebd ) 1. given 2. ( mangle cad=mangle 1 + mangle 2 ) 2. angle addition property 3. ( mangle ebd=mangle 3 + mangle 4 ) 3. angle addition property 4. substitution property 5. ( mangle 1=mangle 3 ) 5. given 6. substitution property 7. ( mangle 2=mangle 4 ) 7. subtraction property of equality which statements could be used to complete the proof? ( \bigcirc ) 4. ( mangle 1 + mangle 2=mangle 1 + mangle 3 ) 6. ( mangle 1 + mangle 3 = 180^{circ} ) ( \bigcirc ) 4. ( mangle 1 + mangle 2 = 180^{circ} ) 6. ( mangle 1 + mangle 3 = 90^{circ} ) ( \bigcirc ) 4. ( mangle 1 + mangle 2 = 90^{circ} ) 6. ( mangle 1 + mangle 2=mangle 3 + mangle 4 ) ( \bigcirc ) 4. ( mangle 1 + mangle 2=mangle 3 + mangle 4 ) 6. ( mangle 3 + mangle 2=mangle 3 + mangle 4 )

Explanation:

Step1: Analyze substitution property

Since \(m\angle CAD = m\angle EBD\), and \(m\angle CAD=m\angle1 + m\angle2\), \(m\angle EBD=m\angle3 + m\angle4\), by substitution property \(m\angle1 + m\angle2=m\angle3 + m\angle4\) (this would be statement 4).

Step2: Analyze substitution property again

We know \(m\angle1 = m\angle3\). Substitute \(m\angle1\) with \(m\angle3\) in \(m\angle1 + m\angle2=m\angle3 + m\angle4\). We get \(m\angle3 + m\angle2=m\angle3 + m\angle4\) (this would be statement 6).

Answer:

1. \(m\angle1 + m\angle2 = m\angle3 + m\angle4\)
2. \(m\angle3 + m\angle2 = m\angle3 + m\angle4\)