Hey there! I'll try to provide you with my best answer.
Answer: ∠a is 20° , ∠b is 130° and ∠c is 50°
If you see more precisely then ΔABC is a complete triangle. And we know that a triangle is 180°. So in respect to ΔABC, we know ∠A and ∠C. So ∠B remains.
∠A is 60° + 30° = 90°
∠C is 70°
∠B is 90° + 70° + ∠B = 180°
∠B + 160° = 180°
∠B = 180° - 160°
∠B = 20°
Now we know that angle a (the corner angle) is 20°. Remaining is angle b and angle c. The ones we actually have to find in the question given.
In one of the small triangle which the,"b" is.
We know ∠a is 20° and the other side is 30°. So the same formula applies again.
∠a + 30° + ∠b = 180°
20° + 30° + ∠b = 180°
∠b + 50° = 180°
∠b = 180° - 50°
∠b = 130°
Now ∠c is remaining. Well all the angles are given again so.. same!
∠c + 60° + 70° = 180°
∠c + 130° = 180°
∠c = 180° - 130°
∠c = 50°
There is another easier way to find ∠c. Line B and C is a straight line so a straight line is also 180°. We know ∠b is 130° so instead of subtracting and switching so much, we can directly subtract it from 180 because they are on a straight line.
∠b + ∠c = 180°
130° + ∠c = 180°
∠c = 180° - 130°
∠c = 50°
The answer is same at the end. Even though this is easier cause we can mentally subtract it instead of going to the triangle formula.
Note: When i show angles with capital letters and small letters, there is a difference. ∠B and ∠b is not the same thing when I wrote it. So please do not misunderstand it. The capital and small letters are clearly shown in the image you have shown.
And sorry for making it so long. I just hope you understood it clearly!! ^^
