Question

Find <1, <2, <3 and <4.

Answer 1

<1=60,<2=60,<3=50,<4=10

Answer 2

Here,

BCD is a straight line and ray AC stands on it.
Hence,
angle ACB + angle ACD = 180° (linear pair property)
=> Angle 1 + 120 = 180
=> angle 1 = 180 - 120
=> angle 1 = 60

Now, in ∆ACB,
angle a + angle B + angle c = 180 (angle sum property of triangle)
=> 60 + angle 2 + 60 = 180
=> angle 2 = 180 - (60 + 60)
=> angle 2 = 180-120
=> angle 2 = 60°

Again, AB is a straight line and rays AC and AD stands on it.
Hence,
60+70+ angle 3 = 180° ( linear pair)
=> angle 3 = 180-(60+70)
=> angle 3 = 180-130
=> angle 3 = 50°

Now, in ∆ ACD,
angle a + angle c + angle d = 180
=> 50+120+ angle 4 = 180
=> angle 4 = 180-(50+120)
=> angle 4 = 180-170
=> angle 4 = 10°

that's your answer.

Hope it'll help.. :-D