Question

use the given information to prove that ( mangle abc = mangle edc ).
given: ( mangle 1 = mangle 4 ), ( mangle 2 = mangle 3 )
prove: ( mangle abc = mangle edc )
step statement reason
3 ( mangle abc = mangle 1 + mangle 2 ) angle addition property

Explanation:

Step1: Use Angle Addition Property

$$m\angle EDC=m\angle3 + m\angle4$$

Step2: Substitute using given equal angles

Since \(m\angle1 = m\angle4\) and \(m\angle2 = m\angle3\), substitute into the above equation.
$$m\angle EDC=m\angle2 + m\angle1$$

Step3: Compare with \(m\angle ABC\)

We know \(m\angle ABC=m\angle1 + m\angle2\) (from given step in problem). By the commutative property of addition \(m\angle1 + m\angle2=m\angle2 + m\angle1\).

Answer:

Since \(m\angle ABC=m\angle1 + m\angle2\) and \(m\angle EDC=m\angle3 + m\angle4\), and \(m\angle1 = m\angle4\), \(m\angle2 = m\angle3\), then \(m\angle ABC=m\angle EDC\) by substitution and the commutative property of addition.