ABC is parallel to DEF and BE = EF. Given that

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KylianneN154408 KylianneN154408

28-10-2022
Mathematics

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ABC is parallel to DEF and BE = EF. Given that

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MarcellinoR551409 MarcellinoR551409 · Answer 1 · 2022-10-28T09:39:34+02:00

[tex]\begin{gathered} \angle ABE=\angle BEF \\ \text{Because they are alternate angles} \end{gathered}[/tex][tex]\begin{gathered} \angle EBF=\angle EFB \\ \text{Because} \\ BE\cong BF \\ \end{gathered}[/tex]

Now:

[tex]\begin{gathered} \Delta BEF\text{ is an isosceles triangle} \\ \text{Besides:} \\ \angle ABE+\angle EBF+\angle EFB=180 \\ 100+2\angle EBF=180 \\ \angle EBF=\frac{180-100}{2} \\ \angle EBF=40 \end{gathered}[/tex]