Answer:
Part a
a = 145°
b = 35°
c = 145°
d = 145°
e = 35°
f = 145°
g = 35°
Part b
a and c
b and 35°
d and f
e and g
Explanation:
When parallel lines get crossed by another line (which is called a transversal),eight angles are formed as in the figure you attached.
Some of these angles are equal
Some are supplementary (add up to 180°)
First let's classify and define the angles so that you understand better
Vertical Angles
These are angles that are opposite each other. They are equal to each other
Thus a and c, b and 35°, d and f, e and g are vertical angles
(Answer to b)
So a = c, b = 35, d = f, e = g
Corresponding Angles
These are angles that have the same position with regards to the parallel lines and the transversal. Such angles are equal
The corresponding angle pairs are:
a and d, b and g, 35 and e, c and f
So a = d, b = g, e = 35 and c = f
Linear Angles
Linear pair of angles are formed when two lines intersect each other at a single point. The sum of the angle measures will be 180°
Here the pairs of linear angles are
a and 35°
b and c
c and 35°
d and e
g and f
e and f
g and d
There are other properties that apply to two parallel lines and a transversal through them but the above two properties are enough to compute all the angles a -g
Let's write down the two properties relating to vertical angles and corresponding angles:
a = c, b = 35, d = f, e = g (1)
a = d, b = g, e = 35, c = f (2)
b =35° and e = 35° and b = g ==> g = 35°
Using the property for linear angle pairs
c + 35 = 180
c = 180 - 35
c = 145°
Since c and a are vertical angles
a = c = 145°
a = 145°
Since a and d are corresponding angles
d = a = 145°
d = 145°
Since d and f are vertical angles
f = d = 145°
f = 145°
So the degree measures of the angles are
a = 145°
b = 35°
c = 145°
d = 145°
e = 35°
f = 145°
g = 35°
You need not necessarily proceed in the same order as I did. Just apply the rules I have provided and you will get the same results
For part b:
The pairs of opposite/vertical angles are
a and c
b and 35°
d and f
e and g