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 $m\angle1 + m\angle2=180$ and $m\angle2 + m\angle3 = 180$.

Step2: Use substitution property

Since $m\angle1 + m\angle2=180$ and $m\angle2 + m\angle3 = 180$, we can say $m\angle1 + m\angle2=m\angle2 + m\angle3$ (Substitution Property of Equality).

Step3: Apply subtraction property

Subtract $m\angle2$ from both sides of the equation $m\angle1 + m\angle2=m\angle2 + m\angle3$. We get $m\angle1=m\angle3$ (Subtraction Property of Equality).

Answer:

$m\angle1=m\angle3$