Question

unit 1 - lesson 7 exit ticket: in the diagram below, $overline{ab}$ is perpendicular to $overline{bc}$ and $overline{be}$ bisects $angle dbc$. if the measure of $angle abd$ is $20^{circ}$ then find the measure of $angle dbe$. justify your answer.

Explanation:

Step1: Encontrar el ángulo ∠DBC

Sabemos que ∠ABC = 90° (ya que $\overline{AB}$ es perpendicular a $\overline{BC}$) y ∠ABD = 20°. Entonces, ∠DBC=∠ABC - ∠ABD.
∠DBC = 90° - 20° = 70°

Step2: Encontrar el ángulo ∠DBE

Como $\overline{BE}$ biseca ∠DBC, entonces ∠DBE=$\frac{1}{2}$∠DBC.
∠DBE = $\frac{1}{2}$×70° = 35°

Answer:

35°