(b)
The 50 degree angle and angle b are vertical angles, which means they are congruent.
The 50 degree angle and angle c are a linear pair, which means that they are supplementary/add up to 180 degrees.
Angles a and c are vertical angles, which means they are congruent.
a = 130
b = 50
c = 130
(c)
The 90 degree angle and angle b are vertical angles, which means they are congruent.
The 50 degree angle and angle c are vertical angles, which means they are congruent.
The 50 degree angle, 90 degree angle, and angle d all form a line, which means that they are supplementary and add up to 180.
Angle d and angle a are vertical angles, which means they are congruent.
a = 40
b = 90
c = 50
d = 40
(e)
The measure of a circle is 360 degrees. These three angles form a circle, so therefore if we add them all up, they will equal 360 degrees.
3a + 4a + 5a = 360
12a = 360
a = 30
(f)
The measure of a circle is 360 degrees. These four angles form a circle, so therefore if we add them all up, they will equal 360 degrees.
3a + 4a + 5a + 6a = 360
18a = 360
a = 20
Hope this helps!! :)