Question

given: (mangle1 + mangle2=180), (mangle2 + mangle3 = 180). prove: (mangle1=mangle3). substitution property of equality: (mangle1 + mangle2=mangle2 + mangle3), (mangle1=mangle3). subtraction property of equality.

Explanation:

Step1: State given equations

Given \(m\angle1 + m\angle2=180^{\circ}\) and \(m\angle2 + m\angle3 = 180^{\circ}\)

Step2: Apply substitution property

Since \(m\angle1 + m\angle2=m\angle2 + m\angle3\) (because both equal 180)

Step3: Use subtraction property of equality

Subtract \(m\angle2\) from both sides of \(m\angle1 + m\angle2=m\angle2 + m\angle3\). So \(m\angle1=m\angle3\)

Answer:

1. Given; 2) Substitution Property of Equality; 3) Subtraction Property of Equality; 4) \(m\angle1 = m\angle3\) (Proven)