Question

In isosceles triangle ∆ABC,
AC
is the base and
AD
is the angle bisector of ∠A. What are the measures of the angles of this triangle if m∠ADB = 110°?

Answer 1

In isosceles triangle ∆ABC,  

AC is the base and ADis the angle bisector of ∠A.

If ∠ADB = 110 then  <ADC=70 (Linear pair of angles )

Therefore <DAC= 1/2(<DBA) (AD is the bisector of <A.)

<DAC + <DBA =180-70 =110

1/2(<DBA) + <DBA=110

<DBA=220/3 and <DAB=220/6

if <DAB=220/6 then <BAC=220/3

<ABC = 180 -(2x <BAC)= 100/3

Therefore the isosceles , ∆ABC,

<ABC=100/3, <BAC =<BCA=220/3