Question

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, then the measure of FEC is
equal to​

Answer 1

Answer:

Fifty five degrees.Right answer

Answer 2

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

$\angle FBC= \angle ABF= x \\ \\ and \\ \\ \angle ACF= \angle FCD= y$

Apply exterior angle property of triangle on ∆ABC

$70° + 2x = 2y \\ \\ or \\ \\ 35° + x = y \\ \\ y-x=35°...eq1$

let us assume

$\angle BFC= r$

Apply exterior angle property on ∆ FBC

$r + x = y \\ \\ or \\ \\ r = y - x \\ \\ r = 35°\:(from\:eq1)$

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

By angle sum property of triangle we can write

$\angle FEC + r + r= 180° \\ \\ \angle FEC + 70°= 180° \\ \\ \angle FEC = 180° -70°\\ \\ \angle FEC = 110°$

Hope it helps you.

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