Question

use the given information to prove that ( mangle2 = mangle3 ).
given: ( mangle aec = mangle bed )
prove: ( mangle2 = mangle3 )
3 ( mangle bed = mangle1 + mangle3 )
4 ( mangle aec = mangle1 + mangle2 )
5 ( mangle2 = mangle3 )

Explanation:

Step1: State the given information

Given \(m\angle AEC=m\angle BED\)

Step2: Use angle - addition property

By angle - addition property, \(m\angle AEC=m\angle1 + m\angle2\) and \(m\angle BED=m\angle1 + m\angle3\)

Step3: Substitute and simplify

Since \(m\angle AEC=m\angle BED\), we substitute the angle - addition expressions: \(m\angle1 + m\angle2=m\angle1 + m\angle3\). Subtract \(m\angle1\) from both sides of the equation. Using the subtraction property of equality (\(a + b=a + c\Rightarrow b = c\) when we subtract \(a\) from both sides), we get \(m\angle2=m\angle3\)

Answer:

\(m\angle2 = m\angle3\)