Question

I is the center of triangle ABC . AI when produced meets the circumference of triangle ABC in D . If angle BAC = 66° and angle ACB = 80° , calculate
(i) angle DBC (ii) angle IBC (iii) angle BID.

Most satisfying answer will mark as brainliest.​

Answer 1

(i)

I is the center of triangle ABC.

=> <A + <B + <C = 180

=> 66 + <B + 80 = 180

=> <B + 146 = 180

=> <B = 34

∴ ∠DBC = ∠DAC = ∠BAC/2

=> ∠DBC = 66/2

=> ∠DBC = 33°

(ii)

=> <IBC = <B/2

=> <IBC = 34/2

=> <IBC = 17°

(iii)

<AIB = 180 - (<IBC + <DBC)

=> <AIB = 180 - (17 + 33)

=> <AIB = 180 - 17 - 33

=> <AIB = 50

Then,

<BID = 180 - 50 = 130°

Therefore, ∠BID = 130°

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