The angle ABC is given, equal to 82 degrees. Through point D, lying on its bisector

The angle ABC is given, equal to 82 degrees. Through point D, lying on its bisector, a straight line is drawn parallel to the line BC and intersecting the side AB at point E. Find the angles of the triangle BDE.

<DBE = <ABC / 2 = 82 ° / 2 = 41 ° (the angle is obtained by dividing the angle ABC by the bisector).

<ADE = <ABC = 81 ° (<ADE and <ABC are the corresponding angles when cutting parallel straight lines).

<BDE + <ADE = 180 ° (<BDE and <ADE are adjacent corners).

<BDE = 180 ° – <ADE = 180 ° – 81 ° = 99 °.

<BDE + <DBE + <BED = 180 ° (the sum of the angles of the triangle is 180 °)

<BED = 180 ° – <BDE + <DBE = 180 ° – 99 ° – 41 ° = 40 °.

Answer: <DBE = 41 °, <BDE = 99 °, <BED = 40 °.