In isosceles ∆dek with base dk , ef is the angle bisector of ∠e, m∠def = 43°, and dk = 16cm. find: kf, m∠dek, m∠efd.

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°

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step-by-step explanation: