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: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is \(m\angle R + m\angle S+m\angle T = 180^{\circ}\), so \(m\angle S + m\angle T=180^{\circ}-m\angle R\).

Step2: Use the given inequality

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: \(m\angle R>180^{\circ}-m\angle R\).

Step3: Solve the inequality for \(m\angle R\)

Add \(m\angle R\) to both sides: \(m\angle R+m\angle R>180^{\circ}\), \(2m\angle R>180^{\circ}\), then \(m\angle R > 90^{\circ}\).

Step4: Analyze other inequalities

Since \(m\angle R>m\angle S + m\angle T\), it is clear that \(m\angle R>m\angle T\) and \(m\angle R>m\angle S\) because \(m\angle S\geq0^{\circ}\) and \(m\angle T\geq0^{\circ}\). Also, since \(m\angle R>90^{\circ}\) and \(m\angle R + m\angle S+m\angle T = 180^{\circ}\), then \(m\angle S + m\angle T=180^{\circ}-m\angle R<90^{\circ}\).

Answer:

• \(m\angle R>90^{\circ}\)
• \(m\angle S + m\angle T<90^{\circ}\)
• \(m\angle R>m\angle T\)
• \(m\angle R>m\angle S\)