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If angle ABC is 100 deg, what is the value of angle ADC? (Note: Diagra

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If angle ABC is 100 deg, what is the value of angle ADC? (Note: Diagra  [#permalink]

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New post 03 Nov 2018, 09:23
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If angle ABC is 100 deg, what is the value of angle ADC? (Note: Diagram is not drawn to scale)
1) Triangle ABC is an isosceles triangle.
2) Angle DCA is 20 deg.

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Re: If angle ABC is 100 deg, what is the value of angle ADC? (Note: Diagra  [#permalink]

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New post 03 Nov 2018, 09:56
If angle ABC is 100 deg, what is the value of angle ADC? (Note: Diagram is not drawn to scale)
1) Triangle ABC is an isosceles triangle.
2) Angle DCA is 20 deg.


Stat 1 is insufficient.

A=c=40
NO inferences can be drawn.
Also Ab=AC since 2 angles can't be 100

Stat 2 is insufficient.
ACd =20. no inferences.


Comibining.
NS
ACD=20
BCD=20

No new inference can be drawn

Hence E answer
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Re: If angle ABC is 100 deg, what is the value of angle ADC? (Note: Diagra  [#permalink]

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New post 03 Nov 2018, 10:02
If angle ABC is 100 deg, what is the value of angle ADC? (Note: Diagram is not drawn to scale)
1) Triangle ABC is an isosceles triangle.
2) Angle DCA is 20 deg.

angle ABC = 100
angle ADC =??

option A: Triangle ABC is an isosceles triangle.
hence angle BCA= angle BAC = (180-100)/2= 40

but we do not know anything about AD, BD and CD...what is the role of them whether they divide each of the angles aor they are just at some angle from each vertices A, B and C

hence option A is not sufficient

Option B: angle DCA= 20
insufficient as it does not give me anything other than providing one angle....
B is not sufficient


Lets combine A and B

if angle DCA = 20 , which means CD is angle bisector...as it bisects angle angle BCA. also considering BD is the perpendicular from B and hence it is the bisector of angle ABC ...in a triangle al bisectors meet at one point which is D in this case

similar is the case with other bisectors and hence angle ADC= 180- (2*20)= 140

Hence C is the answer
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Re: If angle ABC is 100 deg, what is the value of angle ADC? (Note: Diagra  [#permalink]

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New post 03 Nov 2018, 10:05
ans both are Together sufficient 140 deg
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Re: If angle ABC is 100 deg, what is the value of angle ADC? (Note: Diagra  [#permalink]

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New post 04 Nov 2018, 02:23
Using both statement together we can find the required answer

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Re: If angle ABC is 100 deg, what is the value of angle ADC? (Note: Diagra  [#permalink]

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New post 04 Nov 2018, 05:20
By combining two statements, we can only know that CD is Angular Bisector.

Hence, E.
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Re: If angle ABC is 100 deg, what is the value of angle ADC? (Note: Diagra &nbs [#permalink] 04 Nov 2018, 05:20
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If angle ABC is 100 deg, what is the value of angle ADC? (Note: Diagra

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