Question

the two triangles below are similar. also, m∠s = 15° and m∠r = 105° as shown below. find m∠d, m∠e, and m∠f. assume the triangles are accurately drawn. m∠d = ° m∠e = ° m∠f = °

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In \(\triangle RST\), we know \(m\angle R = 105^{\circ}\) and \(m\angle S=15^{\circ}\). Let \(m\angle T=x\). Then \(x + 105^{\circ}+15^{\circ}=180^{\circ}\), so \(x=180^{\circ}-(105^{\circ} + 15^{\circ})=60^{\circ}\).

Step2: Use the property of similar triangles

Since \(\triangle RST\sim\triangle DEF\), corresponding angles are equal. So \(m\angle D=m\angle R = 105^{\circ}\), \(m\angle E=m\angle S = 15^{\circ}\), and \(m\angle F=m\angle T = 60^{\circ}\).

Answer:

\(m\angle D = 105^{\circ}\)
\(m\angle E = 15^{\circ}\)
\(m\angle F = 60^{\circ}\)