Question

the side BC of a triangle ABC is produced to D . the bisector angle A meets BC at E

prove that angle ABC+ANGLE ACD = 2
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Answer 1

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The Triangle and Its Properties

Exterior Angle of a Triangle

The side BC of a ABC is pr...

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Asked on December 26, 2019 by

Pious Rathee

The side BC of a △ABC is produced, such that D is on ray BC. The bisector of ∠A meets BC in ∠ as. Shown in the figure. Prove that ∠ABC+∠ACD=2∠ALC.

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ANSWER

InΔABL

let∠BAL=a&∠BA=b

exterior∠ALC=∠BAL+∠LBA

=a+b

InΔABC

ALbisect∠BAC&∠AC=a

exterior∠ACD=∠BAC+∠ABC

=2a+b

=∠ABC+∠ACo

=b+(2a+b)

=2a+2b

=2(a+b)

=2∠ALC