Question

in ∆ABC, AD IS the bisector of angle BAC and angle ACD= 32°. AD is produced to E such that angle DCE =20°. if angle DAC= 35°, find x and y.​

Answer 1

since AD is the bisector of angle A.
therefore , angle BAD= angle DAC=35degree

In ADC,
angle DAC+angleADC+angACD=180
35 + ADC + 32 =180
ADc=180-67=113

ang.ADB=35+32=67 (exterior angle is equal to the sum of interior opposite angle of a triangle.)

in triangle BAD,
angleB+ BAD +ADB=180
x + 35 + 67 =180
x =180-102=78 answer..

now, angle ADC = y+20
113 = y +20
y=113-20=93answer....