If m∠1 and m∠3 are supplements and m∠2 and m∠3 are supplements, which of the following conclusions is true?
A.∠3 ≅ ∠1
B.∠1 ≅ ∠2
C.∠3 ≅ ∠2
D.m∠1 + m∠2 = 180°

The key concept here is that supplementary angles sum to \(180^\circ\). This means:

- If \(m\angle1 + m\angle3 = 180^\circ\), then \(\angle1\) and \(\angle3\) are supplementary.
- Similarly, if \(m\angle2 + m\angle3 = 180^\circ\), then \(\angle2\) and \(\angle3\) are supplementary.

Now, since \(m\angle1 + m\angle3 = 180^\circ\) and \(m\angle2 + m\angle3 = 180^\circ\), we can infer that \(m\angle1 = m\angle2\) because both are being supplemented by \(m\angle3\). Therefore, \(\angle1\) and \(\angle2\) are congruent.

The correct answer is:

**B. \(\angle1 \cong \angle2\)**

Would you like more details or have any further questions?

Here are 5 related questions:
1. What does it mean for two angles to be supplementary?
2. Can three angles be supplementary in a triangle?
3. How do we prove that two angles are congruent using supplementary angles?
4. What are complementary angles, and how do they differ from supplementary angles?
5. Can an angle be supplementary to itself?

**Tip:** When two angles are supplements of the same angle, they are congruent!

If m∠1 and m∠3 are supplements and m∠2 and m∠3 are supplements, which of the following conclusions is true?
A. ∠3 ≅ ∠1
B. ∠1 ≅ ∠2
C. ∠3 ≅ ∠2
D. m∠1 + m∠2 = 180°

Discover the solution to the problem where m∠1 and m∠3 are supplements, and m∠2 and m∠3 are supplements. Learn the key concepts of supplementary angles and how angles congruence is determined. Ideal for students in Grades 6-8.

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