Question

given: (mangle1 + mangle2=180), (mangle2 + mangle3 = 180). prove: (mangle1=mangle3)

Explanation:

Step1: Start with given equations

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

Step2: Set the two - equations equal to each other

Since both $m\angle1 + m\angle2$ and $m\angle2 + m\angle3$ equal 180, by the transitive property of equality, $m\angle1 + m\angle2=m\angle2 + m\angle3$.

Step3: Apply the subtraction property of equality

Subtract $m\angle2$ from both sides of the equation $m\angle1 + m\angle2=m\angle2 + m\angle3$. We get $m\angle1 + m\angle2−m\angle2=m\angle2 + m\angle3−m\angle2$.

Step4: Simplify the equation

After simplification, $m\angle1=m\angle3$.

Answer:

1. Given; Given
2. Transitive property of equality; $m\angle1 + m\angle2=m\angle2 + m\angle3$
3. Subtraction property of equality; $m\angle1 + m\angle2−m\angle2=m\angle2 + m\angle3−m\angle2$
4. Simplification; $m\angle1=m\angle3$