Question

geometry part 2 ae teacher (acc ed) / logic
m
1
2
n
3
4
p
m∠1 + m∠4 = 180
∠1 ≅ ∠2
∠3 ≅ ∠4
m∠2 + m∠3 = 180

Explanation:

Step1: Analyze the relationship between angles

• Since line \(n\) is parallel to line \(p\), \(\angle1\) and \(\angle4\) are not supplementary.
• \(\angle1\) and \(\angle2\) are not congruent.
• \(\angle3\) and \(\angle4\) are not congruent.
• \(\angle2\) and \(\angle3\) are adjacent angles that form a linear - pair.

Step2: Use the linear - pair postulate

By the linear - pair postulate, if two angles form a linear pair, then the sum of their measures is \(180^{\circ}\). So \(m\angle2 + m\angle3=180\)

Answer:

\(m\angle2 + m\angle3 = 180\)