If $$ m \angle 1+m \angle 2=180 $$ and $$ m \angle 3+m \angle 2=180 $$, then $$ m \angle 1=m \angle 3 $$. Is this statement true? Justify your response.

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UpStudy AI · Accepted Answer

Yes, the statement is **true**. Here's why:

You are given two equations involving the measures of angles:

1. $$ m \angle 1 + m \angle 2 = 180^\circ $$
2. $$ m \angle 3 + m \angle 2 = 180^\circ $$

Let's solve each equation for $$ m \angle 1 $$ and $$ m \angle 3 $$:

1. From the first equation:
   $$
   m \angle 1 = 180^\circ - m \angle 2
   $$

2. From the second equation:
   $$
   m \angle 3 = 180^\circ - m \angle 2
   $$

Notice that both $$ m \angle 1 $$ and $$ m \angle 3 $$ are equal to $$ 180^\circ - m \angle 2 $$. Therefore, they must be equal to each other:

$$
m \angle 1 = m \angle 3
$$

**Conclusion:** Since both angles are supplements of the same angle $$ m \angle 2 $$, their measures are equal. Thus, $$ m \angle 1 = m \angle 3 $$ is indeed true.

**Answer:** 
Yes. Both angles are supplements of angle 2, so they are equal. Therefore, m∠1 equals m∠3.
Yes, $$ m \angle 1 = m \angle 3 $$ because both are equal to $$ 180^\circ - m \angle 2 $$.

If and , then . Is this statement true? Justify your response.

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