Answer:
1. B||C
2.B||D
4.C||D
Step-by-step explanation:
Substituting 10 in for x, the angle next to line b is
7(10)-5 = 70-5 = 65°.
The angle next to line c is
10(10)+15 = 100+15 = 115°.
The angle next to line d is
12(10)-5 = 120-5 = 115°.
The angle next to line e is
8(10)-25 = 80-25 = 55°.
The angle next to line c and the angle next to line d are alternate interior angles. They are inside lines c and d and on opposite sides of line a, the transversal. Since these two angles are congruent, this means that c || d.
The angle adjacent to the angle beside line c would need to be
180-115 = 65°. This is because these are a linear pair, and must sum to 180°.
This angle is a corresponding angle to the angle beside line b; since they are congruent, this tells us that b || c.
Since c || d and b || c, using the transitive property, b || d.
