Segment AK-bisector of triangle CAE. A straight line is drawn through the point K, parallel to the side CA

Segment AK-bisector of triangle CAE. A straight line is drawn through the point K, parallel to the side CA and intersecting the side AE at the point N. Find the angles of the triangle AKN if the angle CAE = 78 °

<KAN = <CAK = 1/2 <CAE – AK – bisector of angle CAE;

<KAN = 78 °: 2 = 39 °;

<AKN = <CAK – criss-crossing angles at parallel straight lines КN and АС and secant АС;

<AKN = 39 °;

The sum of the angles of the triangle is 180 °, therefore:

<ANK = 180 ° – <KAN – <AKN = 180 ° – 39 ° – 39 ° = 102 °.