Question

use the given information to prove that ( mangle 2 = mangle 3 ).
given: ( mangle aec = mangle bed )
prove: ( mangle 2 = mangle 3 )

Explanation:

Step1: Express angles

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

Step2: Substitute using given

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 (\(a + c=b + c\Rightarrow a = b\)), subtract \(m\angle1\) from both sides of the equation \(m\angle2 + m\angle1=m\angle3 + m\angle1\):
$$m\angle2=m\angle3$$

Answer:

\(m\angle2 = m\angle3\) is proved as shown above.