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Answers
Answer:
In a triangle ABC, angle B is twice angle C. AD bisects angle BAC. AB = DC. Prove that angle BAC = 72 degrees?
In triangle ABC, we have
Angle B =2 Angle C
Conside Angle C =y then
Angle B =2y
AD is the bisector of Angle BAC
so, Let Angle BAD= Angle CAD = x
let BP be the bisector of Angle ABC . Join PD.
In triangle BPC,
Angle CBP= Angle BCP =y
BP=PC
Now, In triangle ABP and triangle DCP,
Angle ABP =Angle DCP =y
AB =DC already given
and BP=PC from above
so by SAS congruence creteria,
Triangle ABP congruence triangle DCP
Angle BAP =Angale CDP and AP=DP
Angle CDP=2x Angle ADP=DAP =x {Angle A =2x}
In triangle ABD,
Angle ADC =Angle ABD +Angle BAD
=>x+2x=2y+x
=> x=y
In trinagle ABC we have
Angles A+ B+C =180 degree
2x+2y+y=180 degree
=>5x=180 degree
=>x =36 degree
Hence, Angle BAC =2x= 72 degree
Step-by-step explanation:
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