Triangle ABC is an equilateral triangle then find angle ADC
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michael6891:
we know that we have read in class 9 that if a quadrilateral is drawn in a circle than the opposite angles are equal then Angle B equal to angle D so angle D is equal to 60 degree
sorry angle A equal to angle D
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Answered by
6
Given ABC is an Equilateral triangle
so <A=<B=<C=60°
Now < ABC = < ADC ( These angles stand on the same arc AC)
SO , < ADC = 60°
HOPE IT WOULD HELP
so <A=<B=<C=60°
Now < ABC = < ADC ( These angles stand on the same arc AC)
SO , < ADC = 60°
HOPE IT WOULD HELP
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But sum of opposite angle of cyclic quadrilateral is 180 degree and ABCD is a cyclic quadrilateral so I think angle BDC is 120 degree
yeah u r correct
but u only need ADC
n ADC =ABC
because they stand on the same arc AC
it makes this problem to solve easily
Answered by
7
Hello,
From the figure we can conclude that ABCD is a cyclic quadilateral
Angle BDC = 180 - angle BAC
= 180 - 60
= 120 degree
NEXT JOIN AD
In ΔABD and ΔACD we have
AB = AC ( sides of an equilateral traingle)
∠ABD = ∠ACD (90degree)
AD = AD (common)
⇒ ABD ≅ ACD
⇒∠ADB = ∠ADC
Since both are equal adc = 1/2 of bdc
adc = 60
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