Final answer:
In triangle DEF with DE equal to FD and angle D at 73 degrees, by using isosceles triangle properties, we find that angle F is 34 degrees.
Step-by-step explanation:
In triangle DEF, we are given that line DE is equal to line FD and angle D is 73 degrees. To find angle F, we can use the properties of an isosceles triangle, which states that the base angles of an isosceles triangle are congruent. Since DE is equal to FD, triangle DEF is an isosceles triangle with DE and FD as its congruent sides, and thus angle D (73 degrees) is equal to angle E.
Knowing that the sum of all angles in a triangle is 180 degrees, we can calculate angle F:
- Sum of angles in triangle = 180 degrees
- Angle D + Angle E + Angle F = 180 degrees
- 73 degrees + 73 degrees + Angle F = 180 degrees
- 146 degrees + Angle F = 180 degrees
- Angle F = 180 degrees - 146 degrees
- Angle F = 34 degrees
Therefore, angle F is 34 degrees in triangle DEF.