Questions: Given: angle 1 is congruent to angle 4 Conclusion: angle 2 is congruent to angle 3

Given: angle 1 is congruent to angle 4 Conclusion: angle 2 is congruent to angle 3
Transcript text: Given: $\angle 1 \cong \angle 4$ Conclusion: $\angle 2 \cong \angle 3$
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Solution

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Solution Steps

Step 1: Identify the given information

We are given that ∠1 ≅ ∠4.

Step 2: Determine the relationship between angles 1 and 2, and angles 3 and 4

Angles 1 and 2 are supplementary angles, as are angles 3 and 4. Therefore, m∠1 + m∠2 = 180° and m∠3 + m∠4 = 180°.

Step 3: Show congruence between angles 2 and 3

Since ∠1 ≅ ∠4, their measures are equal. We can substitute m∠4 for m∠1 in the equation m∠1 + m∠2 = 180°. This gives us m∠4 + m∠2 = 180°. We also know m∠3 + m∠4 = 180°. Since both m∠2 and m∠3 sum to 180° when added to m∠4, m∠2 must equal m∠3. Therefore, ∠2 ≅ ∠3.

Final Answer:

∠2 ≅ ∠3

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