Question

find the unknow angles marked in each of the following figures.

Answer 1

here
angle 1= 110
<BAC= 180-110....by linear pair
=><BAC=70°
now <DCA=120°
similarly by linear pair
<BCA=60°
now in triangle ABC
<A+<B+<C=180.....ANGLE SUM PROPERTY

70+<B+60=180
<B=180-130
<B=50°

Answer 2

Here is your answer....

Angle BAC = 180°- 110° [Linear pair]

= 70°

Now,

Angle BAC + x = Angle ACD [Exterior angle property]

=> 70 + x= 120

=> x = 120-70

=50°

And, Angle ACB = 180- angle ACD [Linear pair]

= 180°-120°

= 60°

Hope this helps you....