Question

question △gez≅△vlr. if m∠g = 85° and m∠e = 71°, find m∠r. answer attempt 1 out of 2 m∠r be determined.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In \(\triangle GEZ\), we know that \(m\angle G + m\angle E+m\angle Z=180^{\circ}\).

Step2: Calculate \(m\angle Z\)

Substitute \(m\angle G = 85^{\circ}\) and \(m\angle E = 71^{\circ}\) into the angle - sum formula: \(m\angle Z=180^{\circ}-(85^{\circ}+71^{\circ})=180^{\circ}-156^{\circ}=24^{\circ}\).

Step3: Use congruent - triangle property

Since \(\triangle GEZ\cong\triangle VLR\), corresponding angles are equal. \(\angle R\) corresponds to \(\angle Z\). So \(m\angle R=m\angle Z\).

Answer:

\(24^{\circ}\)