Question

use the given information to prove that m∠1 = m∠3. given: m∠aec = m∠bed prove: m∠1 = m∠3

Explanation:

Step1: Express \(m\angle AEC\) and \(m\angle BED\)

From the figure, \(m\angle AEC=m\angle1 + m\angle2\) and \(m\angle BED=m\angle2 + m\angle3\).

Step2: Substitute into the given equation

Since \(m\angle AEC = m\angle BED\), we substitute the expressions from Step1: \(m\angle1 + m\angle2=m\angle2 + m\angle3\).

Step3: Subtract \(m\angle2\) from both sides

Using the subtraction property of equality, \((m\angle1 + m\angle2)-m\angle2=(m\angle2 + m\angle3)-m\angle2\).
Simplifying gives \(m\angle1=m\angle3\).

Answer:

\(m\angle1 = m\angle3\) is proved as shown above.