△BCE∼△JKL . If m∠B=89° , m∠C=13° , and m∠E=78° what is m∠J ?

1 answer

Given that triangles \( \triangle BCE \sim \triangle JKL \), corresponding angles in similar triangles are equal.

In triangle \( BCE \):

  • \( m\angle B = 89^\circ \)
  • \( m\angle C = 13^\circ \)
  • \( m\angle E = 78^\circ \)

For triangle \( JKL \):

  • The angles correspond to the angles in triangle \( BCE \):
    • \( m\angle J \) corresponds to \( m\angle B \)
    • \( m\angle K \) corresponds to \( m\angle C \)
    • \( m\angle L \) corresponds to \( m\angle E \)

Thus:

  • \( m\angle J = m\angle B = 89^\circ \)
  • \( m\angle K = m\angle C = 13^\circ \)
  • \( m\angle L = m\angle E = 78^\circ \)

So the measure of angle \( J \) is: \[ m\angle J = 89^\circ \]