If m∠1

Question

and m∠3
are supplements and m∠2
and m∠3
are supplements, which of the following conclusions is true?
A.∠3 ≅∠1

B.∠3 ≅∠2

C.∠1 ≅∠2

D.m∠1 + m∠2 = 180∘

Answer 1

To solve the problem, let's analyze the relationships given:

1. If m∠1 and m∠3 are supplements, this means: \( m∠1 + m∠3 = 180^\circ \)

2. If m∠2 and m∠3 are also supplements, this means: \( m∠2 + m∠3 = 180^\circ \)

Now we have the following two equations:

1. \( m∠1 + m∠3 = 180^\circ \) (Equation 1)
2. \( m∠2 + m∠3 = 180^\circ \) (Equation 2)

From these two equations, we can set them equal to each other since both equal 180°:

\[ m∠1 + m∠3 = m∠2 + m∠3 \]

We can subtract \( m∠3 \) from both sides:

\[ m∠1 = m∠2 \]

This tells us that angles 1 and 2 have equal measures, which means:

\[ ∠1 ≅ ∠2 \]

Thus, the correct conclusion is:

C. \( ∠1 ≅ ∠2 \)