Question

in triangle rst, m∠r > m∠s + m∠t. which must be true of triangle rst? check all that apply.
□ m∠r > 90°
□ m∠s + m∠t < 90°
□ m∠s = m∠t
□ m∠r > m∠t
□ m∠r > m∠s
□ m∠s > m∠t

Explanation:

Step1: Use triangle angle sum

The sum of angles in a triangle is $180^\circ$, so $m\angle R + m\angle S + m\angle T = 180^\circ$. Given $m\angle R > m\angle S + m\angle T$, substitute $m\angle S + m\angle T = 180^\circ - m\angle R$ into the inequality: $m\angle R > 180^\circ - m\angle R$.

Step2: Solve for $m\angle R$

Add $m\angle R$ to both sides: $2m\angle R > 180^\circ$, so $m\angle R > 90^\circ$.

Step3: Check $m\angle S + m\angle T$

Since $m\angle R > 90^\circ$, $m\angle S + m\angle T = 180^\circ - m\angle R < 90^\circ$.

Step4: Compare $m\angle R$ with $m\angle S$ and $m\angle T$

Because $m\angle R > m\angle S + m\angle T$, and angles are positive, $m\angle R > m\angle S$ and $m\angle R > m\angle T$ (since $m\angle S + m\angle T > m\angle S$ and $m\angle S + m\angle T > m\angle T$).

Step5: Evaluate other options

$m\angle S = m\angle T$ and $m\angle S > m\angle T$ are not necessarily true (no info on equality/inequality between $S$ and $T$).

Answer:

A. $m\angle R > 90^\circ$, B. $m\angle S + m\angle T < 90^\circ$, D. $m\angle R > m\angle T$, E. $m\angle R > m\angle S$