What are the measures of angles a, b, and c? show your work and explain you answers.

a=30

b=60

c=105

Step-by-step explanation:

The angle labeled a is vertical to 30 degrees. Vertical angles are the angles that happen opposite to each other an intersecting lines.  Vertical angles are congruent.  So a=30.

c and 75 are supplementary because they share the same vertex and are on a straight line together. c+75=180 which means c=180-75=105.

Let's look at b.  The little square box means that angle is 90 degrees. We know the value of a which is 30.  So we have that b+90+30=180 because the interior angles of a triangle add up to be 180.

b+90+30=180

b+120=180

b=60