(deleting when done) what are the measures of angles a, b, and c? show your work and explain your answers.

Angle a is a vertical angle with the 30 degree angle above it. We know two of the 3 angles measures in the triangle, 30, 90 and b. All the angles in a triangle = 180 degrees.

30 +90 =120

180 -120 = 60

The measure of b is 60 degrees

angle c and 75 degrees are supplementary angles since a line is 180 degrees.

we can subtract 75 from 180 to find the measure of c.

180-75 =105

Angle a: 30 degrees

Angle b: 60 degrees

Angle c : 105 degrees