Question

given: ( mangle aec = mangle bed )
answer: ( mangle 2 = mangle 3 )
reason
( mangle aec = mangle bed )
( mangle bed = mangle 3 + mangle 1 )
( mangle 2 + mangle 1 = mangle 3 + mangle 1 )
this line is incorrect.

Explanation:

Step1: Use Angle Addition Property

$$m\angle AEC = m\angle2 + m\angle1$$
$$m\angle BED = m\angle3 + m\angle1$$

Step2: Substitute Equal Angles

Since \(m\angle AEC = m\angle BED\) (given), substitute the expressions from Step 1:
$$m\angle2 + m\angle1 = m\angle3 + m\angle1$$

Step3: Subtract \(m\angle1\) from Both Sides

Using the Subtraction Property of Equality:
$$m\angle2 + m\angle1 - m\angle1= m\angle3 + m\angle1 - m\angle1$$
$$m\angle2 = m\angle3$$

Answer:

\(m\angle2 = m\angle3\)