D is a point on BC such that AD is the bisector of angleA. Show that: angle ADC = 90 + (angleB - angleC)/2

Alex Baird 2022-07-28 Answered
D is a point on BC such that AD is the bisector of angleA. Show that:
angle ADC = 90 + ( a n g l e B a n g l e C ) 2
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Answers (1)

losnonamern
Answered 2022-07-29 Author has 12 answers
e know that
angle ADC = 180 - angle ADB
= 180 - [180 - angle B - angle BAD]
= angle B + angle BAD
= angle B + angle A/2 since AD is an angular bisector
= angle B + (90 - angle B/2 -angle C/2)
= angle B + 90 - angle B/2 -angle C/2
= 90 + angle B/2 -angle C/2
= 90 + (angle B - angle C)/2thus proved
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