Question

in triangle ABC,BC is produced to D.BF and FC arebisector of angle ABC and angle ACD respectively if angleBAC is equal to 70 degree and EF is equal EC and the measure of angle FEC is equal to

Answer 1

Answer:

not understood properly friend ok

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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