Question

finding angle measures of a triangle given two angles of a similar triangle o, m∠c=60° and m∠e=80° as shown below. find m∠w, m∠x, and m∠y. assume the triangles are accurately drawn. m∠w = \\(\square\\)° m∠x = \\(\square\\)° m∠y = \\(\square\\)°

Explanation:

Step1: Encontrar ángulo D en △CDE

La suma de ángulos en un triángulo es \(180^\circ\). En △CDE, \(m\angle C = 60^\circ\), \(m\angle E = 80^\circ\), así que \(m\angle D = 180 - 60 - 80 = 40^\circ\).

Step2: Usar semejanza de triángulos

Triángulos semejantes tienen ángulos congruentes. Así, \(m\angle W = m\angle E = 80^\circ\) (correspondientes), \(m\angle X = m\angle C = 60^\circ\) (correspondientes), \(m\angle Y = m\angle D = 40^\circ\) (correspondientes).

Answer:

\(m\angle W = 80^\circ\), \(m\angle X = 60^\circ\), \(m\angle Y = 40^\circ\)