Question

samara drew two supplementary angles, ∠1 and ∠2. her friend tara also drew two supplementary angles and labeled them ∠t and ∠s. they discovered that m∠2 + m∠t = 180°. select all of the statements that are true. ∠1 and ∠t are congruent ∠1 and ∠s are congruent ∠2 and ∠s are supplementary ∠2 and ∠t are supplementary m∠1 + m∠t = 180° m∠1 + m∠s = 180°

Explanation:

Step1: Recall supplementary - angle property

Since $\angle1$ and $\angle2$ are supplementary, $m\angle1 + m\angle2=180^{\circ}$. Also, since $\angle T$ and $\angle S$ are supplementary, $m\angle T + m\angle S = 180^{\circ}$, and $m\angle2 + m\angle T=180^{\circ}$.

Step2: Use substitution

From $m\angle1 + m\angle2 = 180^{\circ}$ and $m\angle2 + m\angle T=180^{\circ}$, we can conclude that $m\angle1=m\angle T$ (by the transitive property of equality, if $a + b=c + b$, then $a = c$), so $\angle1$ and $\angle T$ are congruent.

Step3: Analyze other angle - relationships

From $m\angle T + m\angle S=180^{\circ}$ and $m\angle2 + m\angle T = 180^{\circ}$, we get $m\angle2=m\angle S$. Then, since $m\angle1 + m\angle2=180^{\circ}$, substituting $m\angle2$ with $m\angle S$ gives $m\angle1 + m\angle S=180^{\circ}$.

Answer:

$\angle1$ and $\angle T$ are congruent; $m\angle1 + m\angle S = 180^{\circ}$