Question

select whether the conjecture is true or false. if ∠r and ∠s are supplementary, and ∠r and ∠t are supplementary, then ∠t and ∠s are congruent. select choice select choice true false need help with this question? get a hint

Explanation:

Step1: Recall supplementary - angle definition

Supplementary angles add up to 180°. So, $\angle R+\angle S = 180^{\circ}$ and $\angle R+\angle T=180^{\circ}$.

Step2: Set up equations

From $\angle R+\angle S = 180^{\circ}$, we can get $\angle S=180^{\circ}-\angle R$. From $\angle R+\angle T = 180^{\circ}$, we can get $\angle T=180^{\circ}-\angle R$.

Step3: Compare $\angle T$ and $\angle S$

Since $\angle T = 180^{\circ}-\angle R$ and $\angle S=180^{\circ}-\angle R$, then $\angle T=\angle S$, which means $\angle T$ and $\angle S$ are congruent.

Answer:

True