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Butoxors [25]
3 years ago
14

PLEASE HELP!!! :))

Mathematics
1 answer:
Nina [5.8K]3 years ago
4 0

For a better understanding of the solution given here please find the attached file which has the relevant diagram.

To answer this question we will have to make use of <u>the Isosceles Triangle Theorem</u> which states that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex angle. Thus, as a corollary we know that is EF is the angle bisector of the vertex angle ∠E, then, EF is the perpendicular bisector of the of the base DK.

Please follow the diagram of a complete understanding of the logic and the solution.

As EF is the angle bisector as given in the question, thus we will have:

m\angle DEK=2\times m\angle DE F=2\times 43^{\circ}=86^{\circ}.

Also, from the Theorem we know that KF will be half of DK and thus, KF will be:KF=\frac{1}{2}DK= \frac{1}{2}\times 16=8 centimeters.

Likewise, from the same theorem we have: m\angle EFD=90^{\circ}

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