Question

the two triangles below are similar. also, m∠x = 60° and m∠w = 80° as shown below. find m∠c, m∠d, and m∠e. assume the triangles are accurately drawn.

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). For \(\triangle WXY\), find \(m\angle Y\).
\(m\angle Y = 180^\circ - 60^\circ - 80^\circ = 40^\circ\).

Step2: Use similarity of triangles

Similar triangles have corresponding angles equal. So, \(\angle C\) corresponds to \(\angle X\), \(\angle D\) corresponds to \(\angle W\), \(\angle E\) corresponds to \(\angle Y\).

Step3: Determine each angle

• \(m\angle C = m\angle X = 60^\circ\) (corresponding angles in similar triangles).
• \(m\angle D = m\angle W = 80^\circ\) (corresponding angles in similar triangles).
• \(m\angle E = m\angle Y = 40^\circ\) (corresponding angles in similar triangles).

Answer:

\(m\angle C = 60^\circ\), \(m\angle D = 80^\circ\), \(m\angle E = 40^\circ\)