Answer:
Step-by-step explanation:
The isosceles triangle, DEK with base DK is shown in the attached photo.
Since DK is the base and triangle DEK is an isosceles triangle, the other two sides, DE and KE are equal.
If EF is the angle bisector of ∠E, then line EF bisects angle DEK into 2 equal angles. So if
m∠DEF = 43°, then
m∠KEF = 43°
m∠DEK = m∠DEF + m∠KEF
= 43° + 43° = 86°
Also, bisector EF divides line DK into 2 equal parts. The means that
Line DK = Line DF + Line KF and
Line DF = Line KF
If Line DK = 16
Line KF = Line DK/2 = 16/2 = 8 cm
Also if m∠DEK = 86°, then,
m∠DEK + m∠EDF + m∠EKF = 180°
This is because the sum of the angles in a triangle is 180
Recall
m∠EDF = m∠EKF
This is because the triangle is an isosceles triangle and the base angles are equal. Therefore,
m∠EDF = m∠EKF = (180 - 86)/2= 47°
Also
m∠EDF + m∠DEF + m∠EFD = 180°
m∠EFD = 180° - (47° + 43°)
m∠EFD = 90°
