Question

In the given triangle ABC, BC is produced to D. BF and FCare the bisectors of ZABC and ZACD respectively. IfZBAC = 70° and EF = EC, then the measure of FEC isequal toAF70°suBсD80°55°110°75°​

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

Given:The given triangle ABC, BC is produced to D. BF and FC are the bisectors of ABC and ACD respectively. If BAC 70° and EF = EC.

To find: Measure of FEC is equal to

Solution:

Let

\begin{gathered}\angle FBC= \angle ABF= x \\ \\ and \\ \\ \angle ACF= \angle FCD= y \\\end{gathered}

∠FBC=∠ABF=x

and

∠ACF=∠FCD=y

Apply exterior angle property of triangle on ∆ABC

\begin{gathered}70° + 2x = 2y \\ \\ or \\ \\ 35° + x = y \\ \\ y-x=35°...eq1\end{gathered}

70°+2x=2y

or

35°+x=y

y−x=35°...eq1

let us assume

\begin{gathered}\angle BFC= r \\ \\\end{gathered}

∠BFC=r

Apply exterior angle property on ∆ FBC

\begin{gathered}r + x = y \\ \\ or \\ \\ r = y - x \\ \\ r = 35°\:(from\:eq1) \\ \\\end{gathered}

r+x=y

or

r=y−x

r=35°(fromeq1)

now since triangle FEC is isosceles triangle, so angle ECF will also be r.

By angle sum property of triangle we can write

\begin{gathered}\angle FEC + r + r= 180° \\ \\ \angle FEC + 70°= 180° \\ \\ \angle FEC = 180° -70°\\ \\ \angle FEC = 110° \\ \\\end{gathered}

∠FEC+r+r=180°

∠FEC+70°=180°

∠FEC=180°−70°

∠FEC=110°

Hope it helps you.

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