Question

determining angle measure relationships
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 triangle - angle sum property

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: \(2m\angle R>180^{\circ}\), then \(m\angle R > 90^{\circ}\).

Step4: Analyze other inequalities

Since \(m\angle R>m\angle S + m\angle T\), then \(m\angle R>m\angle T\) and \(m\angle R>m\angle S\) are also true. Also, since \(m\angle R>90^{\circ}\), then \(m\angle S + m\angle T=180^{\circ}-m\angle R<90^{\circ}\).

Answer:

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