Question

triangle angle theorems proving the sum of the interior angle measures of a triangle is 180° given: y || x prove: m∠5 + m∠2 + m∠6 = 180°

Explanation:

Step1: Use the property of alternate - interior angles

When \(y\parallel x\), \(\angle5\cong\angle1\) (alternate - interior angles). So \(m\angle5 = m\angle1\)

Step2: Use the property of alternate - interior angles

When \(y\parallel x\), \(\angle6\cong\angle3\) (alternate - interior angles). So \(m\angle6=m\angle3\)

Step3: Use the linear - pair property

\(\angle1+\angle2+\angle3 = 180^{\circ}\) (linear - pair property: the sum of angles on a straight line is \(180^{\circ}\))

Step4: Substitute

Substitute \(m\angle1=m\angle5\) and \(m\angle3 = m\angle6\) into \(\angle1+\angle2+\angle3 = 180^{\circ}\). We get \(m\angle5+m\angle2+m\angle6=180^{\circ}\)

Answer:

The proof is completed as above.