Question

In the given triangle ABC, angle ABD = 40°, AB = BC and
AD is the bisector of angle BAC. The measure of angle ADC is
(1) 40°
(2)60°
(3)100°
(4) 75°​

Answer 1

Answer:

hey mate here is your answer:-

Given-AB=BC

angle BAC =BCA(angle opposite to equal sides are equal)

In triangle ABC

angle abc +angle BCA + angle BAC=180°(sum angle property)

let angle BAC equals to BCA is equals to x

40+x+x=180°

2x=180-40

2x=140°

x=140/2

x=70°

it is also given in the question that AD bisect angle BAC

hence, angle BAD=angle CAD

angle BAC=70

2angle CAD=70

CAD=70/2

CAD=35

in triangle DAC

angle A + angle D + angle C=180

35+70+D=180

105+D=180

D=180-105

D=75°

angle ADC=75°

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