A straight line is drawn through the point F of the bisector of the angle BAC, parallel to the line AC

| May 10, 2021 | education

A straight line is drawn through the point F of the bisector of the angle BAC, parallel to the line AC and intersecting the ray AB at point P. Calculate the degree measures of the angles of the triangle APF, if the angle FAC = 20 °.

By condition, point F lies on the bisector of the angle BAC and the value of the angle FAC = 20 °, then, since the bisector divides the angle in half, the value of the angle BAF = 20 °.
Through the point F of the bisector of the angle BAC, a straight line is drawn, parallel to the straight line AC and intersecting the ray AB at point P, in the resulting triangle APF the angle PFA = 20 °, as a cross lying angle FAC = 20 ° at PF || AC and secant AF. Knowing that the sum of the angles in the triangle is 180 °, we find the third angle APF = 180 ° – (20 ° + 20 °) = 140 °.
Answer: the degree measures of the angles of the triangle APF are 20 °; 20 °; 140 °.



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