Question

BAD and ACD are two isosceles . if angle ABD = 64° then find angle DAC.

I need step by step solution plz.

Answer 1

In triangle BDA ,
AB = AD than,
angle DBA = DAB { in triangle , the sides of a triangle are equal than , it's corresponding angle are also equal}
therefore angle DAB = 64° ,
in triangle BAD
angle DBA+ DAB+ ADB = 180°
64+64+ADB =180°
ADB = 180-128= 52 °
again, ADB + ADC = 180° ( linear pair is 180° )
52+ ADC = 180
ADC = 180-52 = 128°
And , in triangle ADC,
AD = CD ( given)
angle DAC = angle = DCA ( equal )= X
X + X + 128= 180
2x = 180-128= 52
X = 52/2 = 26 °

Answer 2

there answer is angle DAC 32 degree