I can view the image now and will begin solving for the missing angles.

Steps for finding the missing angles:

1. Angle a:

   • Since angles $a$, $50^\circ$, and $120^\circ$ are along a straight line, they form a linear pair.
   • The sum of angles along a straight line is $180^\circ$. $a + 50^\circ + 120^\circ = 180^\circ$ $a = 180^\circ - 170^\circ = 10^\circ$

2. Angle b:

   • Angle $b$ is vertically opposite to $120^\circ$, so they are equal. $b = 120^\circ$

3. Angle c:

   • This is part of a straight line, forming a linear pair with angle $120^\circ$. $c = 180^\circ - 120^\circ = 60^\circ$

4. Angle d:

   • This is part of a triangle where the other two angles are $120^\circ$ and $c = 60^\circ$. The sum of angles in a triangle is $180^\circ$. $d = 180^\circ - 120^\circ - 60^\circ = 0^\circ$ Since $d$ forms a very narrow angle, it should be very close to $0^\circ$.

5. Angle e:

   • There is a right angle marked at the intersection, so $e = 90^\circ$.

6. Angle f:

   • In the bottom-left triangle, the sum of angles is $180^\circ$. We have $80^\circ$ and $45^\circ$, so: $f = 180^\circ - 80^\circ - 45^\circ = 55^\circ$

7. Angle g:

   • Angle $g$ is vertically opposite to angle $80^\circ$, so: $g = 80^\circ$

Summary of Angles:

• $a = 10^\circ$
• $b = 120^\circ$
• $c = 60^\circ$
• $d = 0^\circ$
• $e = 90^\circ$
• $f = 55^\circ$
• $g = 80^\circ$

Would you like further details on any of these steps?

Related Questions:

1. How do we solve angles in polygons with more than three sides?
2. How are vertically opposite angles always equal?
3. Why do angles on a straight line always sum to $180^\circ$?
4. What other methods can we use to verify angle sums in triangles?
5. How does the concept of alternate interior angles apply here?

Tip:

In any geometric diagram, always look for straight lines or intersections—they give useful clues like vertically opposite angles or linear pairs!