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In the given figure triangle ABC, BC and FC are bisectors of angle ABC and angle ACD respectively. If angle BAC = 70° and EF=EC, then find the the measure of angle FEC.

In the given figure triangle ABC, BC and FC are bisectors of angle ABC and angle ACD respectively. If angle BAC = 70° and EF=EC, then find the the measure of angle FEC.

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Grade:9

1 Answers

Aditya Gupta
2081 Points
3 years ago
let angle FBC= angle ABF= x and angle ACF= angle FCD= y
we apply exterior angle property on triangle ABC to get
70 + 2x= 2y
or y – x= 35
let angle BFC= p. now we again apply exterior angle property on triangle FBC to get
p+x= y
or p= y – x= 35
now since triangle FEC is isoceles, so angle ECF will also be p.
by angle sum propertyb  we can write
angle FEC + p + p= 180
or angle FEC= 180 – 2p= 180 – 2*35= 110
kindly approve :)

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