Q. 24.4( 44 Votes )

In Δ ABC,

Answer :

Given: B = 45°, C = 55°


To find: ADB and ADC


Explanation:



In Δ ABC,


By angle sum property:


A + B + C = 180°


A + 45° + 55° = 180°


A + 100° = 180°



A = 80°


As AD is bisector of A,


BAD = CAD = 1/2 A


⇒∠BAD = CAD = 1/2 (80°)


⇒∠BAD = CAD = 40°


In ΔADB, we have


BAD+ABD+ADB = 180°


40°+45° +ADB = 180°


85° +ADB = 180°


ADB = 95°


Since ADB and ADC form a linear pair.


ADB + ADC = 180°


95°+ ADC = 180°


ADC = 85°


Hence ADB and ADC are 95° and 85°.


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